Dasha, those are good translations, but you should enter them separately.

Alex, you didn't translate INSTEAD.

The word order with the stressed «со мной» implies ”INSTEAD”.
Perhaps, I should have capitalize ”СО МНОЙ”...

But the meaning is “have lunch with me INSTEAD OF DOING something else” (which wasn’t mentioned here).

Or, looking at it again, “have lunch with ME instead of with someone else” (who wasn’t mentioned here)

Anyway, there's indefiniteness in the phrase, and more context is needed to make a proper translation.

Absolutely

Also, WHY DON’T YOU isn’t literal here - it’s more like an invitation or suggestion.