Three-times repetition offer withdrawn!

I played a game recently and was trying to save the draw. At one point we repeated a position for the third time and the "Claim Draw" option came up, but before I could click on it my opponent made their move and the option disappeared. In the end my opponent blundered and lost, so it didn't cost me anything.

Is this how it's supposed to work, and what should happen in a real OTB game?

I dont think there was position repeated 3 times (when it happens the game immediately ends in a draw), what you saw was a request from ur opponent, a draw request.. it disappears when ur opponent makes a move.

@GyrythII In a real otb game you can only claim on your own time and if it's your move that would make the repetition you have to claim the repetition before you make your move. I suspect (although not sure) if you had pressed draw and then made your move on lichess the game would have been drawn.

@zaak87, that's not true. Once three-fold repetition happens, you get an option to claim the draw or ignore it and play on. It has happened several times to me. @GyrythII's opponent must have ignored it, thus continuing the game.

yes, @GyrythII it is like that sometimes, but I don't know why

@zaak87 Whether a draw is immediately triggered by a 3 fold repetition is down to each user's Lichess settings, I believe by default it is only claimed if you are low on time

@zaak87 I don't think so. I already offered a draw (declined) to prime the engine to look for 3x repetition.
Here's the game- the position repeated at 59, 61 and 65 and the draw offer came up immediately but my opponent moved before I could accept.

@GyrythII
Hi!
This is not three-fold repetition. A three-fold repetition is one when same moves are played for 3 consecutive moves then it is termed as three-fold repetition. It has happened with me also. You can check up my draws at Lichess. They need to 3 consecutive moves only then it would be three-fold repetition.
You mis-understood the term as 'When same position comes up 3 times' instead of the one I mentioned...
Have a good day sir ☺

Actually, with regards to threefold repetition, the moves do not need to be consecutive. See Article 9.2 of the FIDE Laws of Chess:

"The game is drawn upon a correct claim by the player having the move, when the same position, for at least the third time (not necessarily by a repetition of moves):
a. is about to appear, if he first writes his move on his scoresheet and declares to the arbiter his intention to make this move, or
b. has just appeared, and the player claiming the draw has the move.
Positions as in (a) and (b) are considered the same, if the same player has the move, pieces of the same kind and colour occupy the same squares, and the possible moves of all the pieces of both players are the same."

(www.fide.com/FIDE/handbook/LawsOfChess.pdf)

Indeed it doesn't have to be consecutive, but the player can claim draw only when it's his turn to move. In OTB you'd write your move 65.Rd1 on your sheet and then call the arbiter to claim draw. But on lichess it's not possible to do so, unless you've turned on the option to always claim draw automatically. So if your opponent responds fast you won't have enough time to claim draw.
Or at least that's how I think it works. It's a bit of a disadvantage for the person who first stumbles into the 3fold because he will be notified on his opponent's time.