Lemme is an abreviation of "let me". Although used mostly in text, this vocal verbatim is a key component of the language of modern youths. Since the pronounciation of "let me" requires too many syllables, lemme has become an accepted form of expressing this action.
Often used in the phrase "Lemme smash". The calling to your Girlfriend, Wife, or Friends with Benefits requesting sex, as your a horny piece of shit (It often does not work).
There should not be much other reason to use this word than to get some good smash.