I replaced my cross threaded Suntour crankset with a Shimano Alivio crankset, which has much smaller gears. Does this mean that with lowering the front derailleur, I will need to replace my current shift cable with a longer one? If so, how much $ does a typical LBS ask for a good ledgth of cable? Sorry, it seems pretty obvious now that I am typing this, but I would still like to hear what MTB veterans have to say.

The answer probably depends upon how much extra length was left when your current cable was installed. If it is long enough to reach down to the new position of the derailleur, then you're good. If not, then you need a longer cable.

As for price, I typically pay around $6, I think, for Jagwire stainless steel inner cable, which is what I like to use. I've seen galvanized cables go for a couple bucks each.

I charge $3 for the cable and would install it for $10, unless something was really screwed up or weird then there will be a little higher install price.