Well lactose intolerant doesn’t mean you can’t have any dairy at all. I think it means you have to manage your lactose intake. They can still have it in moderation (maybe not everyone, but in a lot of cases)
I’m not east asian myself so I can’t speak from personal experience, but I was listening to this english scholar explain different regions of chinese cuisine and her take is that milk is becoming more popular but cheese is still very niche. Here’s the conversation for anyone who may be interested: www.youtube.com/watch?v=onWbXaRFge0 .