If I understand you correctly, here's a solution:
Suppose we have this data:
Map<String, List<Integer>> map = new HashMap<>();
map.put("Noo", new ArrayList<>(Arrays.asList(8,8,9)));
map.put("No", new ArrayList<>(Arrays.asList(1,8,9)));
map.put("Aoo", new ArrayList<>(Arrays.asList(8,8,9)));
We can filter the data in this way:
map.entrySet().
            stream()
            .filter(e -> e.getKey().startsWith("N"))
            .filter(e -> e.getValue().stream().filter(id -> id <= 7).findAny().orElse(0) == 0)
            .map(Map.Entry::getKey)
            .collect(Collectors.toSet());
The first filter excludes the Names that does not start with "N", the second filter goes through the remaining entries and check if all their ids are greater than 7. In the foreach I just print the data, but you can change the logic to your needs
The result should the this:
Noo [8, 8, 9]