There are 3 different means of transport available from Lanzarote airport to Playa Blanca:
The InterCity bus number 161 departs from the coach station at the airport and makes one stop in Puerto del Carmen before continuing to the bus station (estacion de guaguas) in Playa Blanca. Casas del Sol is about 10 minutes walk from the bus station. Take a look at www.intercitybuslanzarote.es
Taxis are plentiful at the airport, but you may have to queue at peak holiday times. However, taxis can be pre-booked. Take a look at www.lanzarotetaxi.com The cost to Casas del Sol is about 45/50 Euros.
The 2 companies listed below have been used by my previous guests without complaint: