Reddit reviews H.P. Lovecraft: A Life

S.T. Joshi has written one that is generally well regarded

For criticism of HPL's works i would highly recommend:

Dissecting Cthulhu

A Subtler Magick: The Writings and Philosophy of H.P. Lovecraft

Lovecraft: Disturbing the Universe
or any volume in the Lovecraft Annual




For Biography on Lovecraft:

H.P. Lovecraft: A Life

...or the expanded version of the above I Am Providence




And Lovecraft's letters (edited and compiled by Joshi) are really the best way to get deep into Lovecraft, although I'll warn you, you really are reading HPL's conversations with his friends, so there is a tremendous amount of biographical detail, but not a terrible amount in the way of talk about his own work. Some of the best:

Letters to James F. Morton

A Means to Freedom: The Letters of H.P. Lovecraft and Robert E. Howard

O Fortunate Floridian: H.P. Lovecraft's Letters to R.H. Barlow