Cross is hard on shifters, no doubt. I think that the suggestion to wipe the dirt out of the lever is a good first step. Do not use solvents. Once the lube/grease is gone, it is gone. This is a design flaw in my opinion, there should be a lube port. I have also used a q-tip (dry) to get a bit further inside the lever to do some cleaning. Make sure you spin the cotton tight on the q-tip so you do not push some stray cotton into the lever. Cables are also key, gunk in the housing really messes up the works, especially with 10spd due the fact that the tolerances are tight. I always replace cables as a first step using teflon cables then also using that sticky/slick teflon cable lube by finish line. Good luck.