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1.
The right for a team to bat in the last (bottom) half-inning of a baseball game, because the other team batted in the first (top) half-inning to start the game, so that each team gets an equal number of turns at bat.

In an organized game, the home team gets last licks. In informal games, players may forget which team batted first, so near the ending time of a game, a player whose team is behind in the score may call out to remind other players that his team has last licks.
You guys batted first, so we have last licks.
by definite lee July 09, 2006
 
2.
The final hit in a fight or friendly brawl.
What now bitch, I got the last lick.
by Playa1233 May 09, 2006
 
3.
the time when on a birthday or anneversary that you lick your partner in the genital region for the number of years that the day signifies,

"last licks" is acheived when an orgasm is reached on the final lick.
on my 26th birthday me and my girl/guy finally got "Last Licks"
by Konoku Kistune February 14, 2010