Here are some timeshare villa resorts that offer a sandy lakefront beach area. Most don't have lounge chairs on their beaches but do offer sand volleyball nets, playgrounds and/or boat rentals. AFAIK, none of them permit lake swimming (neither does Disney in their lakes). A call to the resorts directly will provide more detail about their beach amenities.
Bryan's Spanish Cove
Simple townhouses located across the street from Vistana, just off i-4 (convenient).
Oasis Lakes Resort
Luxury villas on South Int'l Drive - easy, direct commute to Disney with moderate to light traffic (small sandy area near main pool, if I recall correctly).
Embassy Vacation Resort at Grand Beach/Sunterra Resort Grand Beach (same place)
Spacious villas on Lake Bryan.
Summer Bay Resort
Luxury villas in west Kissimmee, off 192. Nice beach area.
Orange Lake Country Club
Luxury villas around a golf course and lake in west Kissimmee, off 192, with extensive resort amenities.
Marriott Grande Vista
Luxury villas around a golf course and a small lake, on South Int'l Drive. Very nice!
Marriott Cypress Harbour
Luxury 2-BR villas around a good-sized lake, near Sea World. Excellent choice for families.
Hope that helps! Enjoy! Feel free to write me if you wish to rent a timeshare week at a discounted weekly rental rate.
potter@a-o.com