I opened the nVidia X Server Settings panel but didn't find anything in there useful for changing the screen resolution options.  After putting some time into checking the status of things I discovered that the nVidia GPU driver was not even loaded--it was still using the nouveau driver under a restricted feature set.  I was initially impressed by the ability of the Driver Manager to install the nVidia driver with only two clicks, I am now no longer impressed.  The Driver Manager didn't even check the compatibility of the driver with the latest kernel.  The Xorg.0.log file contains the following:

[    32.866] (II) "glx" will be loaded by default.
[    32.866] (II) LoadModule: "glx"
[    33.000] (II) Loading /usr/lib/x86_64-linux-gnu/xorg/extra-modules/libglx.so
[    38.689] (II) Module glx: vendor="NVIDIA Corporation"
[    38.689]    compiled for 4.0.2, module version = 1.0.0
[    38.689]    Module class: X.Org Server Extension
[    38.689] (II) NVIDIA GLX Module  304.131  Sun Nov  8 22:03:20 PST 2015
[    38.689] (==) Matched nvidia as autoconfigured driver 0
[    38.689] (==) Matched nouveau as autoconfigured driver 1
[    38.689] (==) Matched modesetting as autoconfigured driver 2
[    38.689] (==) Matched fbdev as autoconfigured driver 3
[    38.689] (==) Matched vesa as autoconfigured driver 4
[    38.689] (==) Assigned the driver to the xf86ConfigLayout
[    38.689] (II) LoadModule: "nvidia"
[    38.689] (II) Loading /usr/lib/x86_64-linux-gnu/xorg/extra-modules/nvidia_drv.so
[    39.431] (II) Module nvidia: vendor="NVIDIA Corporation"
[    39.431]    compiled for 4.0.2, module version = 1.0.0
[    39.431]    Module class: X.Org Video Driver
[    39.578] (EE) NVIDIA: Failed to load the NVIDIA kernel module. Please check your
[    39.578] (EE) NVIDIA:     system's kernel log for additional error messages.
[    39.578] (II) UnloadModule: "nvidia"
[    39.578] (II) Unloading nvidia
[    39.578] (EE) Failed to load module "nvidia" (module-specific error, 0)
[    39.578] (II) LoadModule: "nouveau"
[    39.726] (II) Loading /usr/lib/xorg/modules/drivers/nouveau_drv.so
[    39.919] (II) Module nouveau: vendor="X.Org Foundation"
[    39.919]    compiled for 1.18.1, module version = 1.0.12
[    39.919]    Module class: X.Org Video Driver
[    39.919]    ABI class: X.Org Video Driver, version 20.0
[    39.919] (II) LoadModule: "modesetting"
[    39.998] (II) Loading /usr/lib/xorg/modules/drivers/modesetting_drv.so
[    40.056] (II) Module modesetting: vendor="X.Org Foundation"
[    40.056]    compiled for 1.18.3, module version = 1.18.3
[    40.056]    Module class: X.Org Video Driver
[    40.056]    ABI class: X.Org Video Driver, version 20.0
[    40.056] (II) LoadModule: "fbdev"
[    40.057] (II) Loading /usr/lib/xorg/modules/drivers/fbdev_drv.so
[    40.087] (II) Module fbdev: vendor="X.Org Foundation"
[    40.087]    compiled for 1.18.1, module version = 0.4.4
[    40.087]    Module class: X.Org Video Driver
[    40.087]    ABI class: X.Org Video Driver, version 20.0
[    40.087] (II) LoadModule: "vesa"
[    40.087] (II) Loading /usr/lib/xorg/modules/drivers/vesa_drv.so
[    40.128] (II) Module vesa: vendor="X.Org Foundation"
[    40.128]    compiled for 1.18.1, module version = 2.3.4
[    40.128]    Module class: X.Org Video Driver
[    40.128]    ABI class: X.Org Video Driver, version 20.0
[    40.128] (==) Matched nvidia as autoconfigured driver 0
[    40.129] (==) Matched nouveau as autoconfigured driver 1
[    40.129] (==) Matched modesetting as autoconfigured driver 2
[    40.129] (==) Matched fbdev as autoconfigured driver 3
[    40.129] (==) Matched vesa as autoconfigured driver 4
[    40.129] (==) Assigned the driver to the xf86ConfigLayout
[    40.129] (II) LoadModule: "nvidia"
[    40.129] (II) Loading /usr/lib/x86_64-linux-gnu/xorg/extra-modules/nvidia_drv.so
[    40.130] (II) Module nvidia: vendor="NVIDIA Corporation"
[    40.130]    compiled for 4.0.2, module version = 1.0.0
[    40.130]    Module class: X.Org Video Driver
[    40.133] (EE) NVIDIA: Failed to load the NVIDIA kernel module. Please check your
[    40.133] (EE) NVIDIA:     system's kernel log for additional error messages.
[    40.133] (II) UnloadModule: "nvidia"
[    40.133] (II) Unloading nvidia
[    40.133] (EE) Failed to load module "nvidia" (module-specific error, 0)
[    40.133] (II) LoadModule: "nouveau"
[    40.134] (II) Loading /usr/lib/xorg/modules/drivers/nouveau_drv.so
[    40.134] (II) Loading /usr/lib/xorg/modules/drivers/nouveau_drv.so
[    40.134] (II) Module nouveau: vendor="X.Org Foundation"
[    40.134]    compiled for 1.18.1, module version = 1.0.12
[    40.134]    Module class: X.Org Video Driver
[    40.134]    ABI class: X.Org Video Driver, version 20.0
[    40.134] (II) UnloadModule: "nouveau"
[    40.134] (II) Unloading nouveau
[    40.134] (II) Failed to load module "nouveau" (already loaded, 0)
[    40.134] (II) LoadModule: "modesetting"

and so on ...  So it appears I will either need to "revert" to the original nouveau configuration and wait for LXLE to provide a loadable nVidia GPU driver or jump through all nVidia's hoops and run their installer.  Maybe I'll have the time to run nVidia's installer at some point but living with this stretched screen resolution (1280x1024 instead of 1440x900) is increasingly difficult by the day--reverting to the original configuration is therefore pretty tempting.  In the process of testing what I thought was the nVidia driver, it now appears that the nouveau disappearing mouse pointer "trick" is related to screen resolution because it has not yet disappeared since the screen resolution was set to 1280x1024.  Of course I'll keep watching it.

Thank you for your reply.  Of course, the Driver Manager asked me for the sudo password before it opened up the panel.  Three video driver choices were offered but two were identical except for '-updates' appended to the title.  Only one was flagged "(recommended)" in green text.  Originally, of course, the "xserver-xorg-video-nouveau" Version 1:1.0.12-1build2 was the selected video driver.  The two clicks were simply to click the "nvidia - 304 (recommended)" Version: 304.131-0ubuntu3 radio button and then click the "Apply Changes" button at the bottom right of the panel.  After the progress bar filled the slot, the Driver Manager panel indicated 1 proprietary driver in use and the radio button for the nvidia - 304 (recommended) option was checked.  To actually activate the driver changes a reboot of the system was necessary.  The first obvious change was all the text indicating the boot progress was much larger than it had been with the default nouveau video driver.  The disconcerting thing was not being able to select the resolution that properly fit my monitor (1280x1024 instead of 1440x900)--the 1440x900 option was no longer available.

Just to verify all this, I opened the Driver Manager (which did prompt for the sudo password), clicked the nouveau driver radio button option and then the "Apply Changes" button to see if it would restore the system to the original configuration.  It quickly did so and rebooting verified that it was so.  Again, with the restored nouveau GPU driver configuration, I opened the Driver Manager (which always prompts for the sudo password) and selected the "(recommended)" nvidia - 304 driver option.  After clicking "Apply Changes" it takes much longer to perform the configurations but eventually completes without any error indications of any kind the same as the first time with the indication that "1 proprietary driver in use."  Rebooting resulted in the same failure to load the nvidia driver as before.  It loads the nouveau driver instead except there is no 1440x900 screen resolution option.  It always selects 1280x1024 even after setting and saving the Monitor resolution to "Auto."  Therefore, whatever procedure was used to prepare the 4.4.0 kernel wrapper with the nvidia proprietary legacy driver for use in Eclectica LXLE 16.04 was done incorrectly so that it repeatedly fails to load during the X server initialization procedures.  Someone needs to fix whatever incorrect procedures were used so that the Driver Manager can install a functional nvidia C51 GeForce 6150 LE legacy driver.  Someone also needs to fix the nouveau 1440x900 screen resolution mode so that the mouse pointer does not disappear after the screen locker activates.  As previously indicated, the mouse pointer doesn't seem to disappear if the nouveau GPU driver screen resolution is set to 1280x1024.  I will continue to perform tests and watch what happens under various conditions.  Since the nvidia legacy driver installed with the Driver Manager fails to load anyway, I will perform further diagnostics using the default nouveau GPU driver.

The repositories have been kept up-to-date almost daily using the ucareupdate utility since Eclectica was first installed.  Ucareupdate was run immediately before performing any of the Driver Manager GPU configurations.  The fact is that the Xorg nouveau GPU driver is faulty and the nvidia legacy GPU driver that loads using the Driver Manager is incompatible with the 4.4.0 kernel.  Both need to be fixed to resolve the Eclectica screen saver induced invisible mouse pointer issue.

Give is a go through synaptic, install the driver that way.

The driver is not specifically built for LXLE its directly from nvidia if it's not working then I'm guessing there is a known bug out there on it.... whats the chip?