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