There are several ways to get to the beaches. If you live in one of the multiple hotels of Castillo del Aguila, you can walk to the nearest beach, Playa Mujeres.
If you have a car, then you have a choice. You can come to the outermost hotel, park along the road (28.859829, -13.797903) and walk.
Or you can drive directly to the beach Playa Mujeres (Playa Mujeres, 28.855045, -13.793006). The last 4.3 km of the road is unpaved and there is a toll.
You can also come to the farthest beach, Playa de Papagayo (28.843607, -13.786818). The dirt road is about 5.8 km and pretty bad.
Playa de Papagayo, for some reason, is considered the best in Lanzarote. In terms of beauty, quite possible, but not as a beach. In addition to the terrible road with a toll, you have to go down a sandy slope, there is very little space and a lot of people. And most importantly, the neighboring beaches, located a couple of hundred meters, have exactly the same water and exactly the same sand.
We swam at Playa Mujeres.