Before de-regulation Pennine used to operate a hourly Skipton - Lancaster service via Settle, Ingleton, and Hornby. The Ingleton - Lancaster section was jointly operated with Ribble.
From a licensing viewpoint, the entire Skipton to Lancaster/Morecambe service was jointly operated by Ribble and Pennine. In practice, the majority of the journeys west of Ingleton were provided by Ribble, and almost all those east of Ingleton by Pennine.
When I was a seasonal conductor at Ribble's Lancaster depot in 1968, Ribble operated two return journeys per week over the Ingleton-Skipton section. They were both on Sundays, the 0948 ex-Lancaster (crew operated! - by Lancaster depot) and 1548 ex-Lancaster (by Ingleton depot - one-man, I think).
Shortly afterwards, I think the 0948 journey became operated by Ingleton depot.
Pennine ran five journeys per day over the Ingleton-Lancaster section, Mondays to Saturdays, and two on Sundays. Of the five M-S journeys, three were operated by Ingleton depot, and two by Skipton. The first journey of the day, c.0700 ex-Ingleton, ran through to Morecambe. I can't now remember whether it did so M-S, or just M-F. The two Sunday journeys were both provided by Skipton depot, the two Ingleton drivers having their one day a week off. At Ingleton, Ribble and Pennine both operated from the same building, which remains in Simpson ownership (the owners of 'Pennine') to this day.
The Skipton to Malham service was also licensed jointly to Ribble and Pennine, but I don't think Ribble actually operated on it.