Well...

I googled something like --> LCM boats given to Iceland, and immediately found that an abandoned one has actually become a "noted landmark," and even a tourist draw. It is on the East coast of the island, in a different location from where you say this is, and it is in very poor condition. So, I doubt the one in your photo is this "famous" one recovered or restored at all. It is most likely another, different boat. However, given the large WWII US presence, and the fact that we left behind surplus items of this nature "all over the world" and the fact that the other one was bought and used by local fishermen, I would bet strongly that this one's story will be pretty much the same. It was most likely "war surplus" that the locals saw some possible use for, and either bought cheaply, or possibly even got for free. As it seems in better shape, it might have served more successfully than the other one in whatever role it was used at before ultimately being laid up.

Links to articles on the "landmark" Icelandic LCM:

https://ancientdan.com/2021/07/12/storming-ashore/

https://www.reddit.com/r/ShipwreckPorn/comments/hq3typ/abandoned_us_navy_landing_craft_in_icelandic_fjord/

https://www.rexby.com/mishamartin/ttd/abandoned-wwii-us-navy-landing-craft

https://www.pixeoapp.com/photo-spots/europe/iceland/wwii-us-navy-lcm-shipwreck/

I noted on Google Maps that Siglufjörður, in the North, has a Herring Era Museum, described as, "Boats, barrels & historic fishing images on display in a former herring salting station & warehouse."

Website:

http://www.sild.is/

Perhaps this boat was also used in the herring industry?