I'm not sure what your concern is. Are you worried that he doesn't like something that many kids like? Are you worried that he is fearful?
Maybe he doesn't like the size of the lake - too big, too much expanse without boundaries, or a fear of the deep water (or the lake grass he senses or the yucky lake bottom). Maybe it's the chaos of the kids running around and screaming, splashing. Maybe he doesn't like the feel of cold water on his skin,or all the sunscreen being lathered on. Maybe he got water in his eyes or nose, or maybe he doesn't like the taste. Maybe he doesn't like the constraints of the life vest. It sounds like he enjoys the on-short activities of playing in the sand. What's wrong with that, other than you paid admission or for a parking pass?
Have you tried water play in a smaller pool in your yard, or sprinkler play? If you don't have this available, what happens if you take him to a sprinkler park? Does he take his shirt off for other activities in other situations, such as running around outside? Does the sand bother him if it gets wet and gets in his bathing suit? What happens in the bathtub?
Right now, he doesn't need swim lessons per se. He needs to feel comfortable in the water, and eventually learn to hold his breath and put his face in the water. Most early swim lessons involve just water acclimation - hold the side of the pool and kick your feet, maybe holding a flotation device (for this age, a wrap-around noodle works for some kids), and "blowing bubbles" by putting your face in the water for just 2 seconds. He's got to do all of that before he works on things like paddling or working on learning anything resembling a stroke.
I'd try some other venues to nail down what the issue is - noise, chaos, sensory issues relating to water, fear of depth, etc. And otherwise I wouldn't push it.
You might try a local Y or community center which is relatively cheap and let them take you on a tour - tell them what the issue is so they don't force him to say he'd like it. Tour during a kiddie swim class so he can see the kids, see the accessories they use, and so on.
I don't think you can force the issue but right now you just don't know enough about what his aversion is, and he's not able to verbalize it. I'd find some other activities for enrichment - most libraries have free passes for museums and science centers and so forth, local farms have strawberry and blueberry picking, some garden centers have animals or petting zoos. Just keep expanding his horizons and don't worry so much about one activity involving the lake.