This point is also relevant with New Year's Eve coming up.
Invite a couple of extra people to your New Year's Eve party whom you might not have thought of inviting, and you might do more good than you think.
It's also worth mentioning that being alone is perfectly fine, but when people become lonely, it's something that needs to be addressed. It's all a state of mind, after all.
A cursory examination will likely not demonstrate loneliness. If I am lonely, then I will be happy when I'm in the presence of any of my friends, and so I'll appear happy and just fine to them. I'll even feel happy, in case they ask me how I am. Loneliness is thus peculiarly difficult to diagnose except deliberately.
[I suppose that once you know this, you might try to detect loneliness as "being really happy to see you" or something. Obviously you might find false positives (being happy for other reasons), or false negatives (if they don't feel you're a very close friend). Still, it's a starting point.
The cure, of course, is to continue to be with your friend for as long as he wants (to the degree possible), let him interact with you, and encourage him to share his feelings and his doings with you. (But no pressure. Encouragement is a friend who's happy to be with you and happy to hear anything you have to say without giving unasked-for criticism, not one who asks you hard questions like "How are you?" Such a question can be helpful to establish that you're interested or willing to listen, but it can also be difficult and annoying to answer, so don't press if he stumbles on it.)
This is kind of a natural resolution, isn't it? I've said that, in response to seeing that your friend wants to be with you, you should continue to be with your friend; and that you should encourage him to share things that he probably would like to share with you (in a way that isn't unpleasant or difficult). This is kind of "duh, that's how to be a good friend", and "that's how to make good conversation, at least in this situation". But it's probably helpful to have things like this written down; not everyone has figured out or internalized every part of it by himself.]
I'm not planning to do anything for NYE myself. I don't particularly even want to be around my family as that can really be not fun at all, further isolation is actually a better option out of those two.
Invite a couple of extra people to your New Year's Eve party whom you might not have thought of inviting, and you might do more good than you think.
It's also worth mentioning that being alone is perfectly fine, but when people become lonely, it's something that needs to be addressed. It's all a state of mind, after all.