The Bible has no answer to this question. We do not the man's name or anything about him, other than that he was a young man.
The importance, then, is not who died, but rather who the murderer was. Lamech was a murderer, just as Cain was. Additionally, we see that Lamech appears to be unrepentant.
It is interesting to note that Cain's response to God's judgment was "My punishment is greater than I can bear". His focus was on his inability to bear up under the punishment for his crime rather than on the horror of his crime. Lamech also appears to refuse to see the evil he has done, choosing rather to wish for an exemption from capital punishment greater than that of Cain.
As an addendum, we know that Lamech did not kill his wife, with whom he was talking, or Abel, who had already been killed previously.