It's maybe just a Carlisle area thing. Carlins are sort of a dried brown pea kinda thing. you soak them for a day,then boil them up with bacon,then eat them with vinegar on.
i've never heard of it either, i live in workington. although i have eaten them raw (when i had good teeth), they were in a mix of pidgeon food stored at my uncles pidgeon loft!!!
i think they a bit like the peas used for peas pudding, ( as in peas pudding hot, peas pudding cold)
i lived in carlisle for 22 years and i had them every year until i was 16 or so. don't know what the easter connection is though (there is one though).
people from troutbeck don't get out much and workington, well, we have all seen the league of gentlemen eh!
Carlins are eaten on Carlin Sunday. I understand it was something to do with a famine. I live in Whitby, North Yorkshire so the custom is quite widespread in the North.