However, we have grown from 20 to now 80 people in our office! [...] How can we organise an effective lunch-time event for 80 people in a small office?
In a few words, you can't. Unless everybody ate on their desks, but that would have little fun and heavily limit the interaction you may have.
I see that the core issue here is that your office is now less adequate for the number of people in it. You basically grew a 400% in personnel, and perhaps what you (or your boss/owner) should be considering is finding a bigger office where you can all fit comfortably.
So, alternatives to having lunch that I can think of include:
Make a reservation at a restaurant where you can all fit and chat comfortably.
Consider having your event at a conference room or hotel, where you will surely fit comfortably and can organize for a catering service for you all to eat.
You could also make your event in the open (like a "field trip" or "picnic"), perhaps some open space or field near your office that can be used. There you can rent some chairs and tables (or well eat on the ground like a real picnic), or also some tent or awning to cover from the sun and elements.