This will allow you to get the list which contains the value you want, and if no-one of the inner lists contains it, it will return a new empty list : 
int val = 10;
List<Integer> innerList = permutationS.stream()    //iterate over inner lists
        .filter(list -> list.contains(val))        //keep one which contains the value
        .findAny()                                 //keep only one if exists
        .orElse(new ArrayList<>());                // if no-one return new List
Example : 
permutationS.add(Arrays.asList(0, 6, 13, 14));
permutationS.add(Arrays.asList(1, 10, 11, 18, 6, 78, 79, 9));
permutationS.add(Arrays.asList(2, 22, 4, 20));
List<Integer> innerList = permutationS.stream().filter(list -> list.contains(10))
                                               .findAny().orElse(new ArrayList<>());
innerList.size(); // = 8
List<Integer> innerList2 = permutationS.stream().filter(list -> list.contains(34))
                                                .findAny().orElse(new ArrayList<>());
innnerList2.size(); // = 0