Let us take it as read that Gomez Addams did indeed kill a lady at some point, and simply managed to talk his way out of a conviction as the Addamses are wont to do. The question then arises: under what circumstances? He's clearly too much of a gentleman to kill out of cruelty. Here are some possibilities that occur to me:
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He engaged in a duel to the death, likely under some sort of adventurous circumstance. Very possibly defending Morticia's honor, or as part of some bloodsport tournament. Almost certainly with swords. Lurch was able to dig up an obscure law relating to consensual duels with melee weapons that Cousin Itt used to successfully prove that Gomez did not technically commit murder.
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He had a long-running game with a very close friend where they would hunt one another for sport, devising increasingly elaborate traps. For years and years they outsmarted each other, with no one coming out on top, until one day the self-assembling IED Gomez fed piece by piece to her pet alligator went off during feeding time. She was never heard from again, but a body was never found and the evidence linking Gomez to the device was circumstantial so the DA couldn't nail the conviction. Gomez is only 80% certain she's actually dead.
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Gomez slit Morticia's throat once during a particularly engaging night of erotic roleplay. This is in and of itself not terribly unusual, but on this particular night they had gotten a little carried away while staying at a hotel in Paris and the maid came in before Morticia had a chance to revive. The case was eventually dropped when Gomez, acting as his own lawyer, called Morticia herself to testify that she was not (or no longer) dead.
