Actually, he wasn't really an influence. Other authors like Dunsany and Machen who Lovecraft encountered after resuming fiction writing did have an influence on later works, but he only discovered Hodgson as late as 1934. By that time Hodgson was too late to be an influence as HPL had been ploughing his own cosmic fictional furrow for a lot of years, and also by which time his fiction career was winding down. But he certainly did appreciate the wide-ranging cosmic perspective of "The House on the Borderland" (which is on the Net in etext form at a couple of places I know of—look up the Litrix Reading Room for one), which may well have been an influence on Lovecraft had he not come to adopt a similarly cosmic viewpoint a number of years earlier.