When you think about it, Betelgeuse has probably been providing or helping Lydia with ghost hauntings for Ghost House and making sure Lydia won't be lacking of "clients" and content for her show.
Beej supporting his wifey even from the Afterlife. The Juice even "hired" a whole department of shrinkers (shrink heads?) to manage all the newlydeads wanting Betelgeuse's professional haunting expertise!
From someone who just stays in his grave, sitting on his ratty couch, in his robe, and searching for potential clients from reading the obituary, probably taking up jobs whenever he feels like it because his profession as a bio-exorcist is uniquely his own and definitely not into the whole bureaucracy crap he did when he was Juno's assistant all those centuries ago, a real loose cannon...
To someone who has his own employees, a huge ass office, and mainstreaming his services where the newlydeads and other ghosts were now demanding his work 24/7!
All those centuries of his bio-exorcist schtick before meeting the Deetz-Maitlands, Lydia especially, and he changed his whole work ethic maybe around the same time he found out about Lydia's new career as a ghost haunting show host and exorcist (maybe not exorcist, but she talks to them and makes the arrangements for both living and dead to coexist).
I won't be surprised if in one of Lydia's visits to the haunted houses, Betelgeuse is there and just watches her work. Maybe make himself appear for a split-second to scare or just "say" hello to Lydia, lol. Betelgeuse is such a sucker for her, so obsessed loyal to Lydia that he didn't even try to make another alive person marry him. If he ever gets married (a second time), it's only gotta be with Edgar Allan Poe's daughter (I'm referring to Lydia, btw).
Anyways, basically they're work spouses. Even though one of them doesn't know it, and the other has been pining for the last 30 or so years.
