Or is it much better to let the lexus dealership deal with something like that?

they can do as good of a job as anyone else can,replacing a battery is relatively a simple job so most repairs shops will be fine for doing this one,and sears sells some real good batteries,the die hard is a real good example of that,its a real good battery to have in a car especially in cold weather,id say they,ll do just fine on doing this,good luck.