"Are you coming over for lunch?" is the best option. "Coming over" is very natural here. We use 'over' to suggest a movement from one part of a place to another. In this case, it would suggest that he's in one part of the city and you're in another, and you're asking whether he's 'coming over' from where he is to where you are in order to have lunch. It's the perfect expression. "Coming in" isn't quite right. What is he coming 'into' exactly? The only way this would work is if he is outside the city, and by 'coming in' you mean 'coming into the city'. [We do use 'come in' for workplaces, however. For example, you might contact a colleague who works part-time to say "Are you coming in for the meeting?"] The third option is fine, but it's slightly less "native". It sounds more natural with 'over'.

Thanks Aud,

Thank you, Chris! :)

#3 is natural and all-purpose. #1 fits calling children inside (from playing in the yard). #2 is regional. Come ..., come here ..., come over here ..., come over ....

Hello, Kimphuc! Thank you. I guess, they are all correct. The difference between 'coming in' and 'coming over' may be in the place you have invited someone to come to. Thus, 'come over' may mean you are waiting someone at your home, while 'come in' at any places inside the buildings. I am not sure, though...