Don't think you can do any 'better' than your lactose-intolerant cop-out.
This is going to sound Buddhist AF, but the problem is that in most cases, it's not the vegans introducing the conflict, but rather this conflict existing within the people who take offense.
They don't feel steadfast in their morals and often don't feel confident in their identity or self-worth either, so when someone comes along who does something they perceive as morally superior, then this confronts them with their internal conflict, which makes them feel like they're being attacked.
So, the two ways to avoid the conflict, as others already suggested, are:
- Never bring up that you're vegan, or
- Give them a reason why you can do the morally superior thing more easily than them.
That you're lactose-intolerant is perfect. Especially with many people not understanding what that entails precisely, you can say that you can't eat many foods anyways, so might as well go vegan. Or that it's even sometimes easier to just pick the vegan variant, as you'll know no dairy is in there.
This is still not easy to use as a cop-out. You'll regularly encounter people who might take offense, and you've got basically just two sentences or so, to defuse that situation. This is why many vegans stop caring, if someone wants to be offended. It's too tiresome to be a people-pleaser.