How to sort a Hashmap<String, List<String>> according to the elements on the list? Java 8

I'm trying to sort this in natural order byKey and byValue using lambda expression and Stream Pipe line Java 8:

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

So, the first part (sorting by natural order) is easy but I am having difficulty with the second part.

The sort should be done by the elements of the list(List<String>) and the result looks like:

input:
{E, [G,B,H]}
{C, [E,A,B]}
{A, [M,D,C]}
output:
{A, [C,D,M]}
{C, [A,B,E]}
{E, [B,G,H]}

The first part of the sort byKey is like:

result.entrySet().stream()
.sorted(Map.Entry.comparingByKey()).forEach(e -> {
System.out.println(e.getKey() + " " + e.getValue() );
});

But as I mentioned before I don't know how exactly do the next step:

result.entrySet().stream()
.sorted(Map.Entry.comparingByKey()
.thenComparing((e1,e2) -> e1.getValue().stream().sorted((s1,s2) -> s1.compareTo(s2)))
)
.forEach(e -> {
System.out.println(e.getKey() + " " + e.getValue() );
});

This lambda expression gave me some compile errors.
Also could you add sources to read about?

You cannot depend on the keys to remain in sorted order in the resulting map since maps are inherently unordered. It may appear to work but it depends on the hashCodes of the keys and other map factors. But for larger maps you cannot depend on it. To solve this you can specify a TreeMap which maintains a sorted order for the keys as then resultant map and use streams to sort the lists.

Map<String, List<String>> map = Map.of("E", List.of("G", "B", "H"), "C",
List.of("E", "A", "B"), "A", List.of("M", "D", "C"));
Map<String, List<String>> result = map.entrySet().stream()
.collect(Collectors.toMap(Entry::getKey,
e -> e.getValue().stream().sorted().toList(),
(a,b)->a, // merge function here, not used but required
TreeMap::new));
result.entrySet().forEach(System.out::println);

prints

A=[C, D, M]
C=[A, B, E]
E=[B, G, H]

An alternative to the above is to sort the Entry based on the key and the specify a LinkedHashMap. LinkedHashMaps retain their insertion order. Everything else is the same as above.

Map<String, List<String>> result2 = map.entrySet().stream()
.sorted(Entry.comparingByKey())
.collect(Collectors.toMap(Entry::getKey,
e -> e.getValue().stream().sorted().toList(),
(a,b)->a,   // merge function here, not used but required
LinkedHashMap::new));
</details>