Lamb street food is one of my favorite restaurants and I go there probably once a week. Here's little bit from their website that I think is spot on:

Lamb, skyr and flatbread are ingredients intertwined with Iceland's food culture and history that should be kept alive. But the food culture is further shaped by foreign influences, as a curious fusion adapts to the tastes of consumers today. LAMB's ideology is precisely to honor Ramm Icelandic traditions and fuse them with centuries-old eating habits in the Middle East. The purpose is to adapt cuisine to changing eating habits, honor the food tradition and support local food production.

We make our daily sauces from skyr and olive oil. We use fresh herbs, coriander and parsley and colorful fragrant super spices such as turmeric, chili, ginger, sumac, zaatar. We bake our own flatbread in the tissues that we roll up with various vegetable mixes of Icelandic quality lamb kebab or for example falafel.

Highly recommend and I've taken all my Icelandic and foreign friends and family there and everyone loves it.

Hope you do too!