I flew in Lanzarote a while ago, 1998. A 172 from an outfit right inside the main terminal at Arecife, I'm sorry I can't remember the name. They were very friendly and pretty informal. The machine, EC-GLL, was mechanically sound but cosmetically iffy. In particular the windscreen was so crazed I had to look out the side when pointing into the sun.
You can fly round the island clockwise, or for a change, anticlockwise. Either way takes about an hour. Fuerteventura is the next island over, only a couple of miles across the water.