Never heard it either. What part of the country/the world does your mother in law come from? It may be possible to trace it (Sounds like a job for Quizmonster!) It sounds related to sayings like ' being in clover' meaning having everything you need, being quids in,being without a care, without having to do anything to be happy (a grazing animal in a field full of clover has excellent food all around it).
There is a plant called 'lamb's lettuce' which is used in salad!
My grandmother used to say 'Sitting there like lamb and salad', meaning sitting there doing nothing, I'm not sure now whether it just meant you were lazy or if it meant you thought you were like lady muck. My grandmother was from the North East too, must be a local saying there!
My mum used to use the expression ‘like lamb and salad’ for sitting around doing nothing
Ashe probably learned it in the 1920s at home in Darlington or in the family village in North Yorkshire