it stands for "down to kill like a motherfucker". origin: New York street gangs
meaning: basically, it's a warning to stay off a gang's turf. it can be seen as a challenge, and if the challenge is accepted, would likely lead to a gang war.
one gang tags a brick wall with dtk (or DTK or d.t.k., etc.). another gang comes by, sees the warning/challenge, and if they accept the challenge, they will tag lamf (or LAMF or l.a.m.f., etc.).
Like a Mother Fucker. Also spelt L.A.M.F. and always capitalized.
Although two current UD definitons have it as 'punk' origin and used in the 70s, it was widely used as early as the 50s in Brooklyn and other areas of NYC and possibly beyond.
Sometimes it accompanied tags of gangs, but mostly it was used as a postscript with tags of gang members or wannabe gang members.
It was also frequently preceeded (separated by a space) by D.T.K. = Down To Kill and followed less often by TTH = To The Heart