As the boss of the Moon/Iriomote stage's Zombie Outbreak in Empire of Cats Chapter 1, Lord Gravey is somewhat like The Face, a powerful wall to keep units from pushing too far. He has very high health and even more when not slain by a Zombie Killer, as he revives with 100% HP instead of the usual 50%. He doesn't burrow, but he has above-average range for a Zombie, a constant attack rate and a 100% chance to inflict knockback, making him very dangerous against slow melee attackers such as Titan Cat and Mer-Cat.
Despite his knockback effect, his backswing buys enough time for more meatshields to enter his range between attacks and thus prevent him from moving, so he's more of a support enemy than a serious threat. And with 250 range and no burrows, one can easily stack Gross Cats, Lizard Cats and Salon Cats on him while he stays in place. Also, since he's often the last strong enemy to go down, fast units like Cow Cat or, later on, Awakened Bahamut can be slipped past him before he revives, destroying the enemy base a little earlier than if you were to wear down his full health pool.
The grave of Doge's father, someone else was buried in it by accident. Was a nice old man with a youthful heart when he was alive, but lost the will to live after being accused of sexual harassment and became a bound spirit.
His Japanese name, Hakate Tarō, is probably a reference to Taro Hakase, or Hakase Tarō in Japanese. It's also a play on words, as Hakate is spelled with the kanji for "grave" (墓) and "hand" or "arm" (手).
His attack animation is kanchō, a Japanese prank which involves using one's fingers to poke the target's behind. Most units don't face the right direction for it to work, but Dancer Cat isn't so lucky.
His Japanese description says that he is a jibakurei, meaning a ghost who can't leave a specific location. In this case, it would presumably be his grave.
He is apparently Miss Haka's husband. Lord Gravey's Japanese description mentions that he was accused of sexual harassment, while Miss Haka's says her husband was taken in for that same reason. Also, their Japanese names share the surname Hakate (墓手).
If counting him as an Empire of Cats enemy, then he and Miss Haka are the only ones to have no variants.