Even if there’s no lid, there’s likely a closed flue dampener. A little door in the middle of the chimney.
Although I’d be incredibly surprised if there’s isn’t a capstone that was put on when the lid was taken off. Unless the lid just broke off and was never replaced…
Are flues water-tight? When I would close the flue in other homes, I would typically hear the sound of metal hitting something hard, which somewhat implies they don’t have a rubber seal.
There are 3 tubes & none of them have caps, so apparently it’s deliberate. Most of the neighbors have no caps either and I think most fireplaces are blocked off in the region.
Smoke rises and goes through those fine even tho their narrow. But rain almost never falls perfectly straight down, so the amount of rain that gets in those three narrow pipes is incredibly minimal.
If the fireplace was still open with the tubes it wouldn’t be an issue what little water might come in would just evaporate.
It’s probably ok. But you usually see that method in Europe or upper east coast America in historic homes.
You’re probably better off asking a neighbor, or if you’re really worried, just call a chimney inspector so you know for sure