This is about the trinity of trinities – 3 x 3 making 9 (lives) – and the number 9 being a lucky number.
The domestic cat’s inquisitiveness leads her into hazardous situations from which she is able to extricate herself through toughness, athleticism and some luck. It was believed that cats had more than one life.
In ancient times, the domestic cat was considered lucky. They thought that cats had nine lives because nine was considered a lucky number being the ‘trinity of trinities’.
‘Trinity’ is the 3 persons of Christ: the father, son and holy spirit. The trinity of trinities must be 3×3=9.
I cannot explain, and think it is irrelevant to explain, what the trinity of trinities means. For this explanation it is a simple mathematical formula describing the perceived exceptional luck of the cat.
P.S. The Japanese maneki neko is their lucky fortune cat bringing luck to their owners.