sorting a json array using java 8 stream api

Probably you are looking for code like this:

objectsArray.stream().sorted(
    Comparator.comparing(a ->  Double.valueOf((String)((JSONObject) a).get("distance")))
).forEach(o -> System.out.println(o));

The casts that we are using are the following:

((JSONObject) a).get("distance")) //to get the distance as an Object

and then

((String) ((JSONObject) a).get("distance"))) // this Object is actually a String, so cast to it

and then

Double.valueOf((String)((JSONObject) a).get("distance")) //this String, however, is a double, and we want to compare the double size, not alphabetically 

Cause you'd need to compare based on the double value of the distance.

However, there are multiple things to improve. As we are using OOP here, it probably makes sense to at least convert the "String" stream to some objects that'd make sense.

EDIT:

Here's how you probably should have done it:

//define a class to conform with OOP stuff
public static class Coordinate {

    private final Double lat;
    private final Double lon;
    private final Integer type;
    private final Double distance;

    public Coordinate(Double lat, Double lon, Integer type, Double distance){
        this.lat = lat;
        this.lon = lon;
        this.type = type;
        this.distance = distance;
    }

    public Double getDistance() {
        return distance;
    }
}

// define a conversion logic
private static Coordinate convert(JSONObject raw){
    Double distance = Double.valueOf((String) raw.get("distance"));
    Double lon = Double.valueOf((String) raw.get("lon"));
    Double lat = Double.valueOf((String) raw.get("lat"));
    Integer type = Integer.valueOf((String) raw.get("type"));
    return new Coordinate(lat, lon, type, distance);
}

then your method is as easy as writing:

List<JSONObject> coordinates = (List<JSONObject>)new JSONParser().parse(objects);
List<Coordinate> sortedCoordinates = coordinates
                .stream()
                .map(raw -> convert(raw))
                .sorted(Comparator.comparing(Coordinate::getDistance))
                .collect(Collectors.toList());

Another tip I have for you is using a better library like https://github.com/FasterXML/jackson for your object mapping.