It is possible to get up to three times higher prices for live lobsters than lobsters that are sold frozen, according to the episode Krossgötur on Rás 1.
It discusses a so-called lobster hotel in Höfn, which is run by Matís. At the lobster hotel, lobsters are kept alive for a certain period of time from the time they are caught so that they can be sold when demand is higher.
You can listen to a review of the lobster hotel here.