I have read what's translated of the LNs. It's jolly good stuff, really, even if occasionally morbid. Better written than the other LNs I've read (though they aren't many). The anime was faithful to the source. Bits and pieces were cut, mainly stuff concerning other characters than the Nazarick folks (that is, concerning the original denizens of that world). They were probably cut because they are only really meaningful for later parts of the story. This is the exceedingly ordinary situation when there are no plans whatsoever to continue the anime beyond the initial run, so anything not relevant to it can be cut.

I won't describe it any further to avoid spoilers. I'd suggest reading it from the beginning. Just skip chapters covered by the anime if you want.