We'll be getting a coach transfer from Lanzarote airport to Playa Blanca. Should we take our baby car seat for the transfer journey? We haven't booked an airplane seat for the baby so does that mean we may not have a seat space for her on the coach?
According to https://www.busbud.com/blog/travelling-spain-bus-need-know/ your answer depends on what company and class you'll be traveling.
The Premium Class Provides Baby Seats.
Regardless, I would check with your travel agent to confirm seating for your child, and make sure they know that you are traveling with a baby so preparations can be made.
Even if you don't need it on the coach, might you need it for driving once you reach your destination?