The Cripple was the only name given to the Cat's mother.
When the two factions of Felis sapiens built two arks and left Red Dwarf, they left behind those members of their society who were considered sick or disabled. They were abandoned to fend for themselves and slowly started to die off. The Cripple was one of those left behind ("Waiting for God").
She met and became friendly with a Cat that was nicknamed the Idiot, who was abandoned because he was mentally handicapped. They started to come together for companionship and eventually had a child who would grow up to be the Cat.
The Cat had trouble remembering his parents, but did remember a woman who rejected his advances and became quite angry at him, hitting him with a frying pan (Infinity Welcomes Careful Drivers).
Behind the scenes
It is reasonable to assume from her nickname "the Cripple" had some trouble walking. Her fate was never explicitly mentioned, but she almost certainly died before the Cat Priest.