Lanzarote is not a well-known hiking destination. Most people land on this Canary Island to enjoy sun and sea.
With a good map and some time you will find nice niches on this island. For instance the string of volcanic pimples in the black sea of solidified lava in the Parque Nacional de Timanfaya. Or the naked and arid hill ridges in the south. Also, the coastline has some nice corners, but for the endless string of holiday resorts.
Check the complete list of Canary Islands.