AFAIK if the LCD can display the resolution then it will work, if your LCDs native resolution is 1024x768 then most likely when you set it higher, its just scaling the image to fit the screen effectively leaving you with 1024x768. Try 1024x768 and the higher resolution and see if you can read small text with the higher resolutions because if it IS scaling then most likely small text will be distorted.
Also, what is the brand and model of the LCD TV?