There actually should be a way for it to give damage, Tene tested lava ladders and it worked fine. In addition, gilguy has been killed by it in quite random incidences.
sooo lava boat is OP at the moment, with the updated version where u can "walk on water" u litterally cannot take damage from lava wether u walk on it, its dumped on ur head, or u want to go for a nice swim. this is causing issues in gym battles and such and has been pointed out to me by a few players. sooo yea thats bout it.