In the poker variant of Texas Hold 'em, The "Big Lick" refers to holding a six and a nine as your two hole cards. In sexual terms, when a man and a woman, two women, or I guess two guys are performing oral sex on one another at the same time, this is referred to as a "69". As with the "Big Slick", the "Big Lick" often produces fortunes to be lost when gambling.
In gambling, if someone, hopefully a woman, has a 6 & 9 in their hand then you would say they have the "big Lick". Even better is if someone has pocket 6 & 9 and they pair up with a 6 & 9 on the table (flop, turn, or river) then that is called a "Poker Orgy".