OP, my dd18 has Lyme. She was diagnosed 2 years ago, but sick much longer. I'm happy to help you if you have any questions about navigating the parks.
We did rent a wheelchair a couple of years but my dd is pretty small, the chairs were uncomfortable and the cost to rent day after day was the same as buying a 'transport chair'. These are smaller versions of wheelchairs but don't have the large wheels in the back. I'm not sure about your ds's strength but my dd is very weak all over so no way was she going to push herself around. The transport chair is lightweight, and inexpensive. For the cost of renting a wheelchair for one trip, she now owns a chair she can use for getting around the resort, getting through the airport and using at home to go to the museum or zoo. So, just something to consider...We have used it for 3 Disney trips now plus a few around town trips.