java-how to manage multiple lists of data- in a single variable- with easy access to each list

I would declare my variable as:

List<List<DataType>> lists = new ArrayList<List<DataType>>();

There is a slight time penalty in accessing list methods through a variable of an interface type, but this, I think, is more than balanced by the flexibility you have of changing the type as you see fit. (For instance, if you decided to make lists immutable, you could do that through one of the methods in java.util.Collections, but not if you had declared it to be an ArrayList<List<DataType>>.)

Note that lists will have to hold instances of some concrete class that implements List<DataType>, since (as others have noted) List is an interface, not a class.

List is an interface. ArrayList is one implementation of List.

When you construct a List you must choose a specific concrete type (e.g. ArrayList). When you use the list it is better to program against the interface if possible. This prevents tight coupling between your code and the specific List implementation, allowing you to more easily change to another List implementation later if you wish.

If you know a way to identify which list you will be dealing with, use a map of lists.

Map<String,List<?>> = new HashMap<String,List<?>>();

This way you would avoid having to loop through the outer elements to reach the actual list. Hash map performs better than an iterator.