A Church Grim (AKA Kirk Grim) is a kind of supernatural black dog. Unlike most other kinds of supernatural black dogs, this one is a guardian spirit, rather than an aggressive four legged embodiment of your imminent death.
Let's say you're an early Christian. You've just completed building your new church, cemetery included, and old Mr. grapples-with-wolves up the road has finally got himself killed after years of wolf wrangling. What do you do?
Why, find a pitch black dog and bury it alive before burying the other guy, of course!
Cemeteries needed a guardian, because if there wasn't a guardian around to protect the newly dead, Satan himself could just waltz right in and take his pick of the ectoplasmic litter. The first thing buried in a new cemetery was the volunteer. In order to save a human being from the job, a pitch black dog was chosen. It would die, then rise up in spirit to keep the satanic riff-raff out of the church and the cemetery.
Similar practice was done to a lamb, only instead of guarding against the devil, the lamb would ensure that nothing catastrophic would happen to the church-building itself.
Seeing a spectral Church Grim is- if not straight up bad luck, then at least a portent of a Significant Event. Seeing the lamb signals that a child is going to die. Both of these points are moot if you are the minister of the church in question, in which case you'll just be wondering who the hell keeps letting these animals wander around your church yard.