Now I'm wondering what the longest Underground trip is without visiting a given line more than once. Probably needs a rule about the District and Circle lines where they overlap since you could get a lot of mileage out of that.
(I calculated the shortest one that includes all lines back in the early 2000s but they've obviously changed things around since then.)
My gut feeling would be Chesham/harrow/rayners lane/hammersmith/edgeware/earls court/green park/stockwell/embankment/elephant/bank/aldgate east/liverpool st/bond street/baker/kingsx/cockfosters
A route out to Epping via Newbury Park would be another option though, probably elephant/bank/kingx/green park/bond instead.