Try going into the LG's Picture menu. There should be an option for Aspect Ratio. Select "Just Scan" and exit out. That fixed my issue with my LG 47LH90 what is connected to a GeForce 9600GT DVI port via a DVI/HMDI adapter.
You cannot make your HDTV 2560x1600. The number of pixels are fixed an cannot change. All large HDTVs have resolutions of 1920x1080. Smaller HDTVs are around 1366x768. You can use a resolution smaller than the HDTV's native resolution, but not higher.
Actually it is possible to use a resolution higher than 1080p, but the entire desktop will not fit on the screen so you need to pan around desktop to look at things that are "off screen".