One doesn't read a classic English mystery story for the puzzle, as perplexing as that might be, but for the wonderful settings and characters. Lord Peter, Albert Campion, and Marsh's Roderick Alleyn are all not just great detectives but fascinating people that you would love to have as friends. What makes Marsh especially strong is how much detail she gives to her supporting cast.
The Lampreys are all perfect jewels of the story tellers art. They are the classic eccentric, down on their luck, British nobility. Too busy being noble and sincerely lovable to remember to be practical. They are all charming, and your heart will also go out to Roberta Grey, one of the Lamprey's particular friends.
Other reviewers have gone over the plot, so I'm not going to bore you with details. Suffice it to say you will be alternatively delighted and and horripilated (I think that's the word) as the book moves from light hearted comedy to a rather ghoulish end game. Everything the mystery addict could ever want!
There are many good reasons to read this book. It is one of the novels that helped define the British mystery story doyen. Ngaio Marsh is on of the most important writers in that genre (even if she isn't quite British), and Death of a Peer is certainly one of her best books.
But the real reason to read it is that it is simply very, very good. If you have never read a Marsh book this is a great way to start. If you have, you know what you're missing.