He just stopped showing up but he occasionally makes a rare appearance when it’s funny.

From 1980 onwards, he was gradually phased out of the main cast, with his appearances becoming increasingly sporadic; for instance, he did not appear in any strips between December 25, 1981, and June 27, 1982. He had largely disappeared from the comic by April 24, 1983, his last regular appearance, and his disappearance was not fully elaborated upon at the time. Lyman has made three cameo appearances in the comic since then. First, in the strip on Garfield’s 10th birthday, June 19, 1988, where he appears in the title panel seated between Jon’s father and Liz Wilson; he also appears in a flashback panel within the strip. The next two were on April 2, 2013 and June 23, 2024, in a picture on the newspaper Jon was reading.

According to Davis, Lyman’s original purpose was to be someone who Jon could actually talk to and express other ideas — a role gradually taken over by Garfield himself. Once Lyman was no longer needed for that purpose, he was removed without explanation. Jim Davis has jokingly given explanations about Lyman’s sudden disappearance and long absence from the strip; examples include “don’t look in Jon’s basement” and “he joined the Peace Corps and was never heard from again.”
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After decades of absence, Lyman made his big comeback in the Garfield Show story arc, “Long Lost Lyman”. In this continuity, it is revealed that he found work as a wildlife photographer. He had gone to Australia and searched for a mythological creature, but suddenly disappeared without a trace. When Jon, Garfield, and Odie went searching for him, they had found him dressed as that creature. Lyman explained that he never contacted them, because there was no way he could. Lyman decided to stay in the jungle to protect the wildlife from poachers, but promises to visit when he can.

https://antifandom.com/garfield/wiki/Lyman

According to Garfield’s Scary Scavenger Hunt, this is what happened to him:

It was an official flash game, so take that as you will for canonicity.