you should move your ltc to another wallet some blocks after the fork happened. wait for some blocks more. Then in a new LCC wallet (if any) import your old wallet keys.

Keep in mind that:
a) many people will do this, get their LCC and sell them fast for some other altoicoin, just like you.
b) this means that the price of LCC will drop like a rock.
c) you will probably not be that fast to make any money
d) there is no such thing as free money. forks are like printed fiat money: inflation, not a generation of wealth. Printing money doesn't generate wealth, it only takes wealth from those who have it to those who print it.
e) By the time you do this, the price of LTC will have dropped due to people like you who wanted LTC only for the airdrop, selling their LTC and switching back to the coins they had before the fork.
f) Any money you get from selling your LCC will be far less than the money you will lose from the price drop of LTC. It's a zero sum game.

P.S.: In the good scenario that some exchange will accept and create LCC pairs, if they don't you're left holding the bag.