You will need to search the U.S. Copyright Office records to determine for sure which of Lovecraft's books are in the public domain in the U.S.
All of his works published before 1923 are in the public domain in the U.S., but there seems to be some question as to whether his later works had the required copyright notices or not, and whether the copyrights on his later works were renewed.
If the copyrights were renewed, the books published after 1923 would be under copyright protection for 95 years after their publication and would not yet be in the public domain in the U.S (as they are in European Union countries).
Some of the phrases in Lovecraft's books have been trademarked, by the way, but that alone should not interfere with the making of audio books.
Go to
U.S. Copyright Office for information on how to search the Copyright records.
Good luck.