Loneliness is a contributing factor to declining cognition & overall health, especially in the elderly. And it’s wonderful that your father is able to express his needs & wants to you.

If you father is an animal lover & there is a shelter in your area they may need volunteers to pet the cats & socialize the kittens (much easier than walking shelter dogs).

What about finding an older woman to be a paid companion - cooking a meal, a bit of housekeeping, and genuine conversation? You would want to brief the person about your father’s loneliness. You could introduce her as someone for him to “get to know” - which is true. Fortunately he’s from the generation where politeness & boundaries come fairly naturally. She may be able to find out what the underlying concern is. Is he loneliest at night? Does he miss home cooking? Does he want someone to sit & watch TV with him? Depending how impaired he is this type of companionship in-home on a regular basis may be sufficient. You would need to monitor closely & of course the companion would need to be aware of his wanting to “date” someone. A short walk in the yard/neighborhood or maybe a chaperoned trip to a casual restaurant might help as well.

The idea is to present the companion help as another lonely person. If he belongs to a church there may be someone there who does home companionship visits.

I’m sure others in this group will have some excellent ideas for you.