I’m not sure what this means.
It’s quite possible that a sewer line (a ‘lateral’, as opposed to the ‘main’ running down the street) could be installed that runs from the barn to the either the house or directly to the municipal sewer main in the street. Depends on the exact situation and you’d need to get an engineer/contractor to take a look at your place to know if it’s possible. If so, I don’t know why you’d need a chamber or anything. But it might need a pump, depending on the slopes.
The other main option is a septic system; you’d need a bit of open space with appropriate soil, but if the property is big enough to have a barn that’s far enough from the house to want a bathroom, you’ve probably got room somewhere. Again, you’ll have to get someone out to look at your place to know what the exact possibilities are.
I don’t know much about composting toilets.
I suppose a port-a-potty or something is also a possibility, but I suspect that’s not something that would work for you.