Yes a lipo will work.. I have 2 mini lsts and I run everything in them. If you dont install a lipo cut off with the stock esc, just be aware of your run times (depending on mah of course). I dont run a cut off, but something I usually do, is if I am messing around with some buddies that are driving thier 18t"s or whatever with similar mah nimh packs.. Make sure they holler at you as soon as they feel thier packs starting to lose a little juice.. then dont get greddy. Turn her off and go to the charger, or stick in a freshy. If you want the cutoff, they are like 30 bucks.. I personally think its kinda of a waste.. Just be aware of your runtimes and you should be fine. I think the highest maj lipo for a mini lst is about 2000mah. Tha should give you a good 10 mins, depending on how much foot you have in it.. er woops, I mean finger in it..
Also, Your wheel problem could be a number of things.. I think the diff and trannys in these little trucks are the weak link, I you are going to be running lipos and hotter motors, you may want to rebuild them with the MIP kits that are offered. I did it to one of mine and it is bomb proof now.