Always rent with Sixt. One of the only locations where Sixt is not directly at the airport, probably because all the space at the airport was already taken up. Short shuttle ride, easy to find (at the shuttle bus station in the first row and on the way back you get dropped of right in front of the terminal). Clean office, parking right in front. Good selection of cars. Efficient and kind staff.
A little on driving on Lanzarote. Parking is almost always easy and driving is layback. Because of the substantial amount of biking tourists, roads mainly in the south of the island are “via cyclista” with a limit of 60 km/h. Pay attention to set speed cameras that are indicated well and very visible (also because there’s a solar panel sticking high above it). New are the average speed checks that are a little less visible. There are about four I think, mainly on roads that are next to main roads that for that reason sort of turned into bike paths, for instance from El Golfo to Playa Blanca (LZ-701 next to the LZ-2). If the road is empty the 60 limit seems pointless, so it’s risky if you miss the cameras and they’re not as obviously pointed out as the regular cameras.