Yes you can develop a lactose intolerance. That’s what happened to me. There are regular milks that are advertised as lactose free, and to me they taste the same as the usual cow’s milk. I like oat milk better so I tend to stick to that. Personally I make an exception for cheese, as I don’t like many cheeses and the substitute made it worse, but I make sure to consume very little. I can have some without having issues, but that may be different for you!
Definitely worth experimenting!