What is the highest possible rating on Lichess?

There is no limit

This makes me think of Claude Bloodgood

Copy and paste from Wiki below
"Bloodgood organized chess games within Powhatan Correctional Center in Powhatan, Virginia, which were by necessity with fellow inmates.[3] Many of these inmates were taught the game by Bloodgood, and thus began as unrated and inexperienced players. Bloodgood obtained USCF memberships for them. Some accused Bloodgood, with his intimate knowledge of the rating system, of rigging their ratings. The accusation was that he arranged for new prisoners to play rated games against other prisoners, who would deliberately lose, thus giving the new inmate an inflated USCF rating. Bloodgood, it is further alleged, then played rated games against the new highly rated prisoner, and each time he won, gained a few more rating points. This continued for several years, and by 1997 his rating rose to 2759, making the 59-year-old Bloodgood the second highest rated player in the nation, only behind Gata Kamsky. In comparison, at his retirement Bobby Fischer's rating was 2760, and several leading grandmasters were in the 2600s.

This is all a matter of considerable controversy even today. Bloodgood himself vehemently denied these accusations, and said that he played chess in the only competitions available to him, prison tournaments, and won almost every game because he was the strongest player in the prison system. As his rating rose, he wrote the USCF to warn them that its system was prone to "closed pool" ratings inflation. But nothing was done until Bloodgood's rating skyrocketed. By virtue of his high rating, Bloodgood would have qualified for entry into the U.S. Chess Championship, a prestigious invitation-only event intended for the best 16 players in the country. This caused an investigation by the USCF, which debated extensively what to do about the situation. In the end, Bloodgood wasn't invited to the event (which he could not have attended anyway), and the USCF changed its ratings system rules to attempt to prevent "closed pool" ratings inflation from prison memberships."

https://en.wikipedia.org/wiki/Claude_Bloodgood

#22 - Interesting article... Thanks for the post. :]

Well, I saw an account which began win 1000 rating in those games and 800 in puzzles.

Refuting my initial argument that there is a limit: I negelected to account for minimum rating gain for a win. So if someone never loses, they will in fact continue to increase their rating, regardless of who they play. This would also refute my argument about the draw limits of the game because a theoretical 5000+ rated AI system could continue playing lower rated opponents to accumulate wins/rating points even if playing equally matched opponents always resulted in a draw/0 points.

@oberschlumpf I think there is a maximum difference of 400 rating points and a minimum rating gain of ~0.08 per game. i.e. If you are rated 2250, all of your opponents will effectively be considered at least 1850.

On lichess even 2 persons could apply the bloodgood scheme.
They each make an account: A and B. B wins all games until B = 1800 and A = 1200.
Now player 1 abandons account A and opens a new account C. C wins all games against B, until C = 2100 and B = 1500.
Now player 2 opens a new account D to 2400, the 1 opens E to 2700 then 2 opens E to 3000, then F to 3300, then G to 3600...