El Lago is along the road connecting Arrieta and Punta Mujeres. Most likely you'll drive along this route going from the Jardin de Cactus and the stunning Jameos del Agua. My advice is enter the town of Arrieta and drive along the coast until you see El Lago on your left. The address lists it as Calle de Los Morros 27, but note that you'll see 26 and 28 on your right separated by nothing and get confused - just keep driving another minute until the road bends right and it is there.
The higher rated option in the area is El Amanecer (according to TA, both seem to have equivalent good mentions in recommended restaurant lists) but that is closed on a Thursday.
Also notable is that El Lago does not have a website. As per usual I've taken a picture of the English version of the menu.
- Fresh Marinated Anchovies - fresh butterflied anchovies in olive oil, garlic & vinegar. A far difference from the canned or salted kind with large chewy pieces and a light tart vinegar;
- Steamed Mussels - excellent chewy sweet mussels allowed to be alone with their own juices rather than the typical white wine & garlic. Some weren't debearded but that's the way it goes sometimes;
- Fresh Grilled Pompano - a local fish half grilled perfectly on both sides to create a salty burnt skin on one side and a tender strong pure flesh on the other. The first time I've been served proper Canarian potatoes warm in their wrinkles skin.
Lastly the Canarian typical sauces of Mojo Verde and Mojo Roja are the best versions I've tried. Especially the Verde has a punchy garlic and coriander taste which was great on bread.
Next time I would order any local seafood that they recommend. There are too many choices on the menu to select - be aware that some fish are caught immediately local whilst a lot of others are imported from Morocco (which is very common in Lanzarote and I suppose they do share an ocean) whether it matters to you or not.