Many birds that mate for life can and do die from loneliness. They will pine away, losing interest in life if they do not find a mate. I keep lovebirds too, and hence the name Lovebird, they are very suseptable to dying if you do not find them a mate. I have seen them die this way.
I think your best course of action is to find this bird a mate. You have nothing to lose at this point, and if he is truly suffering from loneliness, he will not reject a new bird. If you do get another bird, introduce them very slowly. Don't just plunk her in. Keep her where he can see her so he thinks he is finding her and whooing her. You also don't want the other bird to suddenly attack him as this can happen.
You might also try taking the place of a mate. Sounds crazy, but I have kept single Lovebirds alive by winning over their hearts. Spend a lot of time with this bird. He may be very skittish at first, (I don't know how tame he is), but you can get him out of this environment and into your living room. Get to know him and let him get to know you. Spend quality time with him and he may warm up to you enough to consider you his mate. I did this with several Lovebirds that I didn't have a mate for and their lives were quite enriched being able to interact with human surroundings.
You can also put some stuffed animals in his cage or even an over turned feather duster in the corner so he thinks there might be another feathered bird nearby. Some sort of white noise never hurts either. Some quiet music always calms my parrots down here in the house.
You might also PM GrandmaBird here. She is the Button expert and might have a bird source for you.
Good luck!