I'm in agreement with Paulie about the Mastil. Also we loved Portofino and La Pardela (what a fantastic fillet Oporto). Lollipops all round, service second to none, cleanliness 100% sparkling clean.
Lani's a tad expensive, but you get what you pay for - mouth watering swordfish au gratin - fabulous service.
Went to an English place just by the beach (not going to mention the "watery" name) had one meal (the most expensive of all our 3 course meals during our stay) messy plastic table cloth was wiped with dirty cloth/ food was average (ie Beefeater on a busy night). We decided to give it a second chance by going in for a drink the following week (well it was convieniently located), but unfortunately after over 10 mins we left because no one had even approached the table to ask us if we wanted to order and there was no one working behind the bar!!! Oh and just a last dig if I may, it was the only restaurant whose advertising boards had spelling mistakes "SATUDAY NIGHT ENTATANMENT" and this an english place - I hold my head in shame! LOL
Seriously - you're in Lanzarote - go Spanish!