I had occasion to look into this question as I just listed the home at 13133 Alton Rd in the Alton Developement in Palm Beach Gardens.
Yes, The Club at Alton does have a lap pool located outside the main club house 13255 Alton Rd, Palm Beach Gardens, FL 33418.
The Club at Alton features a Grand Hall with lounge seating & TV, Chill Zone with Bar Area, Refrigerator, Sink & Flat Screen TVs, Health Hall with Free Weights, Strength & Cardio Training Equipment, Boxing bag and Interactive Training, Tot Room, Aerobics Room with ballet/fitness Barre, Spin stations & other workout essentials, Resort-Style Heated Pool w/ Lap Lanes, Beach Entry and cabanas, Tennis & Pickleball Courts, Full Basketball Court, Sand Volleyball Court, Kids Playground, Outdoor Game Tables (foosball and ping pong) and On-Site Managemen