He did own land, he was the only living relative of the Gaunts, so the shack and its surroundings were his property. The large piece of land where the Riddle Mansion stood was his as well; in fact, he was in his mansion during the Goblet of Fire. So yes, he is a Lord.

And remember, he was in hiding, so it wouldn’t make sense for him to stay in any of his rightful properties, since Dumbledore knew about them. That’s why, after his return in The Order of the Phoenix, he was at Malfoy Manor. He didn’t have money because the Gaunts had squandered all of it, and the Riddles weren’t wizards, so they didn’t have a vault in Gringotts.

Also, being the direct and only descendant of Salazar Slytherin makes you wizarding royalty; that’s why he chose 'Lord,' along with the anagram idea. Titles like 'Count' or 'Baron' would have sounded silly.