By Live Lite, you mean Ableton? Well, Reaper is a full-featured DAW, not a "lite" version. And Ableton is in version 8 now, so that one isn't up-to-date. I'd keep Reaper.
As Abletons a lite version it would be best as a tool in the arsenal rather than your main DAW...so Id say Reaper as well...though why cant you install Live too? even the lite version is great for sketches and getting ideas down??
i only really use Live but I could agree with that, if its just for two tracks it could possibly seem overcomplicated....folks have to remember though that the session view is essentially the same as any other traditional DAW and it does have an excellent audio warping ability that would beyond Reapers capabilities...that being said if your a half decent musician you wont need it, me Im less than half decent lol