You need an ImmutableMap full of ImmutableList instances. Use Guava to preserve your sanity.
To start off, create ImmutableList instances that you require:
ImmutableList<String> list1 = ImmutableList.of(string1, string2, etc);
ImmutableList<String> list2 = ImmutableList.of(string1, string2, etc);
Then create your ImmutableMap:
ImmutableMap<String,List<String>> map = ImmutableMap.of("list1", list1, "list2", list2);
There are numerous ways to instantiate your immutable lists and maps, including builder patterns. Check out the JavaDocs for ImmutableList and ImmutableMap for more details.