java lambda - how to traverse optional list/stream of optionals

First, check if the Optional is present. If yes, then stream the list and filter the non-empty ones and print each of them.

optionalList.ifPresent(list -> list.stream()
            .filter(Optional::isPresent)
            .map(Optional::get)
            .forEach(System.out::println));

Almost similar for the stream case too

optionalStream.ifPresent(stream -> stream
            .filter(Optional::isPresent)
            .map(Optional::get)
            .forEach(System.out::println));

You can indeed stream the Option<String> and filter only non empty values.

Optional<List<Optional<String>>> optionalList = Optional.of(Arrays.asList(Optional.empty(), Optional.of("ONE"), Optional.of("TWO")));

optionalList.orElseGet(ArrayList::new)
            .stream()
            .filter(Optional::isPresent)
            .map(Optional::get)           
            .forEach(System.out::println);

You can also use Optional.ifPresent() as suggested in another answers :

optionalList.ifPresent(l -> l.stream()
                             .filter(Optional::isPresent)
                             .map(Optional::get)                               
                             .forEach(System.out::println));

Personally I prefer the first way because it removes a nested level : I find it more pleasant to read.