"I would like to have the ability to be able to add say the Fruit list
and maybe meat b to the favourites list so I dont have to keep going
through the complete lists"
Well, this is up to you. You are going to have to write some code. You can write it to work any way you want.
Neither JQM nor jQuery provide any support for local storage. You will have to work that out yourself, perhaps choosing a cross-platform local storage library to use.
You can certainly keep both local storage and the list(s) in sync - so that when you add a favorite you add it both in local storage and in the DOM, and when you delete an item from favorites, you delete it both from local storage and from the DOM. You just have to write the code to do it. But it really is not worth the hassle. It's much easier just to create the lists from local storage on
pagebeforeshow.
Anyway, neither jQuery Mobile nor jQuery have any magic bullet to write your code for you.