obj.user = {
    "10": {
        "500": {
            "rank": "LEADER",
            "nick": "test1"
        },
        "501": {
            "rank": "MEMBER",
            "nick": "test2"
        }
    },
    "20": {
        "500": {
            "rank": "LEADER",
            "nick": "test1"
        }
    }
}

var userCache = {}
function checkUser(chat, id, callback) {
    if(userCache[id] === undefined) {
        request(apiURL, function(err, res, body) { // возвращается json
            userCache[id] = body;
            console.log(id + " NEW");
            callback();
        })
    }
    else {
        console.log(id + " OLD")
    }
}

Object.keys(obj.user).reduce((promiseChain, chat) => {
    return promiseChain.then(() => new Promise((resolve) => {
        for(var id in obj.user[chat]) {
            checkUser(chat, id, resolve);
        }
    }));
}, Promise.resolve());