forgive me if i seem short, but the reason people usually try to avoid redundantly give the same info out, is that when you try to search the forums, you get alot of random post that are just tid bits oh the whole process.
Like i said in my post, search the forum for optimus m stock roms, download this and open it, it's just a zip file. In this file you will see a folder called system. In that folder you will see app. The filesystem for android is based on unix, which linux is a "free" version of. So the root of your file system on android will be "/"
so the file in the rom zip will be in directory /system/app/
the full path will be /system/app/lghome.apk
you can navigate to this folder and just drag the file out to extract it. Where ever you pulled the file out remember the file path.
Reboot your phone into recovery from the powered off state by holding menu, vol down, and then holding enter. Hold these till you see the recovery boots up. Navigate the menu to the mounts with the volume buttons, and depending on the recovery you are using, press home or the camera button to make the selection. Find the option that says "mount /system"
once this is done you can connect the usb. Open your command terminal and issue this command "adb push c:\path\to\lghome.apk /system/app" where c:\path\to\lghome.apk is the directory path to lghome.apk.
If this file is on your desktop you can do "adb push %userprofile%\desktop\lghome.apk /system/app/"
after this is done issue the command "adb shell reboot" if all is well, your phone will be good to go.
If you have a recovery that does not support mounting the system partition, there is a command to mount it through adb shell.
You could always reflash the rom, but learning to fix stuff the hard way is how you will really learn :d
and i do see the error in my first post "adb lghome.apk /system/app/" should have been adb push lghome.apk /system/app/", i'll fix that for good measure