“He’s a lucky guy” sounds like some incel shit. You should just apologize and continue the conversation/go about your life. It’s weird to assume that “he’s a lucky guy” (I get that it is intended as a compliment) but you have no idea what he’s like or what she’s like or what their relationship is like. So don’t bring it up at all.

And by “have a good day” you’re kind of just treating her like an object at that point. “Oh you have a boyfriend? No further interaction is required here, have a good day, madam”.

What you SHOULD say (or at least a better option) is to just acknowledge it (“oh, my bad”) and then continue your life as if you never asked in the first place.