"With the lunch we drink wine."
No because the word order is incorrect. The 2nd part of the sentence needs to be a verb making 'trinken' go before 'wir'. Otherwise, 'wir' would be the second part of the sentence.
WAS IST DENN LOS??!!! what's wrong with “Zum Mittagessen”?!! ... =/
This really must be fixed to reflect that "zum" is a correct shortening of "zu dem."
Right. The verb is always in the second "position" of the sentence. Don't ask me why, I don't know why, but that's the way it is. In this case "mit dem Mitagessen" is the first, meaning the verb has to be second, forcing wir to go after. I think one of the only exceptions to that is the command form, where the verb is in the first "position".