" An extensive list of parish register transcripts and indexes publications is available from the Cumbria Family History Society." (Page on CASCAT headed "Guide to Church Records")
Cumbria Family History Society
https://cumbriafhs.comChoose heading"Shop" to see list of publications, then select a category. I had a quick look but saw no mention of Our Lady and St. Joseph. Transcriptions are done by volunteers.
Another source of free to view online transcriptions of parish registers is the Online Parish Clerks projects. This is also done by volunteers and is organised by county. (I make extensive use of Lancashire Online Parish Clerks, known as LANOPC, which is excellent and well-advanced.) Look at the list of resources under Cumberland on the English counties board to see if there's a link to Cumbria or Cumberland Online Parish Clerks. If there's no link then just google Online Parish Clerks Cumbria. LANOPC began with C. of E. registers and have only recently added some Catholic and Non Conformist ones.
If the registers are not online you could ask someone planning a visit to Carlise Archives to do a look-up. Post a request on the Cumberland board. Study the catalogue entries for Our Lady & St. Joseph in CASCAT before you frame your request since the years you want searched might be in more than 1 volume or run of registers. There are also missing years.
The baptisms you want should have mother's maiden name and state if the child's parents were married ("conjugam" or "conj" in Latin). Child's, parents' and godparents forenames might be in Latin or English, depending on the custom of the priest. Surnames will be in English.
Researching Catholic family history in England is not straightforward.
Lots of guidance on Catholic FHS and GenGuide websites.