I recently spent a week in Iceland. What a wonderful landscape. There is a saying that if you get lost in Iceland, just stand up! Unfortunately, I had bad weather, but the experience was a joy. Excellent huts that are fully equipped. I took my own dehydrated food but there was no need to take stove\pots.
Check out some photos. There is a lot of info on the web re this trail, so I will save my typing fingers!
https://www.ultimategearlists.com/destinations/laugavegur-trail-iceland