Probably needs checking on the ground.
OS OpenMap Local (April 2024) suggests "Tythebarn Lane" (one word with a y) and there is a "Tythe Barn Cottage" (two words with a y) https://www.openstreetmap.org/way/662674262 (and another "Tythe Barn Cottage" https://www.openstreetmap.org/way/662674259 which may also need checking as it seems unlikely that there are two cottages with the same name