ひげが長く腰が曲がっている様子が老人を連想させる事から長寿を祈願したもの。

Ebi-no-yakimono has been eaten to pray for a long life because the shape of a lobster with its long antennas and curved waist is similar to that of an aged person. - Wikipedia日英京都関連文書対訳コーパス

木造阿弥陀如来坐像（重要文化財）－恵心僧都（源信）がクリの巨木から作ったと伝えられる丈六の阿弥陀如来像で、この仏に祈ると腰から下の世話をかけずに往生できるといわれる。

Wooden seated statue of Amida Nyorai (Amitabha Tathagata) (Important Cultural Property) - a statue of Joroku, which is considered to be full-scale, having one jo and six shaku (or about 4.8 meters), holding a legend that says Eshin Sozu (Genshin) created this statue out of an enormous chestnut tree, and the worshipers of this statue of Buddha can pass away without having any problems below the waist. - Wikipedia日英京都関連文書対訳コーパス