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.).