I was pointed to this book by the most glowing review I have ever read in the New Yorker. The gist was that the whole is greater than the sum of the parts, and that over the course of four collections of stories, a very full character is painted. I would agree with that. These stories feel very autobiographical, some, especially for their brevity feel like they capture an event that has just occurred - almost impressionistic. At the end, we have a very good feeling for a character, whether this is Lydia or not, is sort of moot. That's a pretty significant literary achievement.
Here's the problem. This isn't the world's shortest book. I think what is actually the case is that the fourth collection is really a great book and that LD has significantly grown as a writer into probably a major writer. That isn't really evident in the first two collections, and while reading them gives you further depth of attachment to the character, I'm not sure it's time optimally spent. I've got Faulkner's Collected and Borges Collected stories sitting on the shelf ignored while I pass them over for a very enthusiastically reviewed orange tome. Ok, that's not a particularly fair comparison, but hey, it's what happened.
There are great moments in each of the collections, but those moments are very close together in the final collection. How Shall I Mourn Them is heartbreaking, and a good example of how appropriate a literary experiment is to grieving. There is so little comforting at the moment of when pain feels so particular and personal in recognizing how common rending grief is. The uniqueness of an experiment seems absolutely right. Barthelme's The Dead Father has something of the same feeling.
A nice common thread throughout is Issa and his gentle and minutely observed humanity. The influence shows early on, and the feeling in the beginning is how pleasant it is to reintroduce this style, but how difficult it is to be a disciple of his. By the end, LD seems to be Haikuist of similar empathy and observational power. That's no mean feat.