Lord John and Private Matter is a mystery, involving the titular character after leaving the Scottish prison, and returning to London. There are multiple suspects and intrigues, a few deaths, and whores galore.
I got the sense that this was a side of London Gabaldon wanted to write about, but it didn't fit into the story of Claire and Jamie. So she wrote about Lord John, and gave him the reins.
I feel neutral about Lord John. I don't like him nor dislike him. He doesn't come across as having much personality. He seems subdued and empty-like.
The mystery was intriguing. The explanation was really long, in Outlander fashion. The beginning of this story was a bit confusing with the different names and references, but it becomes easier as the book progresses.
As a standalone book, I wouldn't recommend it to someone who hasn't read Outlander. There's not enough exposition or background. However, if you're an Outlander fan there's no need for that. The story starts right away.