We got the lift up as one of our party was on crutches. We only paid for the adults and the kids were free. You access the lift via a very long tunnel from the sea front which the kids were convinced they had seen on Dr Who (it's metal and the lights change colour). Once at the top the views are spectacular in all directions. We decided to walk down, but be aware the route is not well signposted. Follow the signs from the carpark for West Walls Walk and even though this looks like it is going back up to the castle it is the way down. There are multiple paths through gardens and the back streets of Alicante but if you keep going down hill you will eventually find your way.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.