My first instinct was to suggest a Stream of the input Map‘s entrySet which maps the values to new values and terminates with collectors.toMap().
Unfortunately, Collectors.toMap throws NullPointerException when the value mapper function returns null. Therefore it doesn’t work with the null values of your input Map.
As an alternative, since you can’t mutate your input Map, I suggest that you create a copy of it and then call replaceAll:
Map<String, Double> adjustedMap = new HashMap<>(someMap);
adjustedMap.replaceAll ((k,v) -> v != null ? 2*v : null);