Without other context in this question, it is hard to figure out what you are trying to say. My best guess is that you are making a statement about James. Since he has been lonely recently, it might be a good idea to meet up with him so that he feels he has people that he can lean on.
If this is the case, I also guess that you will need to ask the second question in a negative way. This means the question becomes “Why not…?” If you want James to meet you, there are a variety of verbs that fit the blank.
You could choose between some of the following: have, invite, ask, etc.
The round at the end of the sentence is actually colloquial slang. Most of the time we would say “around”, meaning to having someone around you. If you speak more quickly, you may end up dropping the “a” at the beginning of the word.
Instead of meaning that James is round, it means that James is around, or that James is present near you. The proper writing of this should actually include an apostrophe (‘) in the place of the a because that letter has been omitted.
The sentence should then become something like this example:
James is rather lonely these days. Why invite him ’round?
