How can I negate a lambda Predicate?

You would have to do .filter(((Predicate<String>) String::isEmpty).negate())

If you want, you can define

static<T> Predicate<T> not(Predicate<T> p) {
    return t -> !p.test(t);
}

and then

.filter(not(String::isEmpty))

but I would just stick with v -> !v.isEmpty()