There is a great restaurant in a town called Nazarath. Built out of/into the lava.
Rumour has it that Omar Sharif won it in a game of backgammon.
There is a lunar landscape (lava fields) with a museum and a restaurant that uses the Earth's heat to cook, they also make mini geysers with water poured down holes in the ground.
Cesar Manrique Lanzarote artist
for some more touristy things. I've been to the Mirador, the caves and the cactus garden.
You can also do a day trip to a little island just off the coast.
I haven't been there for over ten year when I used to go paragliding, some great cliffs and hills, it seemed very strange to find seashells in the ground 2000 feet up!
It can be very windy there!