Why Can't I offer a Draw in the game I'm playing against the in House engine at it's highest level ?

I think that this controversy is getting out of hand. Seems to me that the OP is very good and it's true that his moves are different than the computer ones and also have clear very human like plans. He's smart and I can tell he worked very hard. respect!

engine moved a pawn on move 87 and 133 so way do you feel you can clame a draw?

Lichess has advanced software in which it refuses to even let cheaters offer draws to other fellow computers.

I mean, a draw offer doesn't make a difference, just role play that the computer would refuse all draws. On the other hand, an arbiter is important, like if you make 50 move rule for example or stalemate then it has to admit the draw.