Is it legal to buy Litecoin and sell those within a few minutes? In US, is it legal to buy and sell cyber currency within a few minutes?
I cannot think of any law it would violate.  But legal advice needs to come from a lawyer who you hire.

Note that if you sell it for more than you paid to buy it, regardless of how long you held it, you need to report it on your tax return as a capital gain, and pay the appropriate taxes.  (If you sell it for less, you may be able to deduct a capital loss, subject to a variety of restrictions.)