That I don't know, but it seems to far removed, so I would imagine they don't.
But if they do, the cycle lane from Lewes is really not that far, is only very gently uphill, and you wouldn't have to pedal much at all after the game! There is easy parking on the outskirts of Lewes.
The A27 DOES have a cycle lane, all the way into town to the west, all the way to Lewes in the east. Halfway between Falmer and Lewes there is a road parallel to the A27 - farm access, I think - but you could park your car there and cycle to the ground. It's probably only 20 minutes walk, to be...