moment().format("LTS") returns a string value in hh:mm:ss AM/PM format. When you create a moment object using a string that is not in standard format, you should pass the input format as second parameter to moment constructor.

For eg: Jan 1, 2017 in string 01012017 is not a standard representation. But if you need a moment object out of it, using moment("01012017") will give "Invalid Date" response when formatting. Instead, use moment("01012017","DDMMYYYY")

var d = moment("01012017")
d.toISOString() => "Invalid date"

var d = moment("01012017", "DDMMYYYY")
d.toISOString() => "2016-12-31T18:30:00.000Z"

In your code, when creating 'date' variable pass "hh:mm:ss A" as second parameter in the moment constructor as mentioned below .

   var date = moment(startdate, "hh:mm:ss A")
        .add(seconds, 'seconds')
        .add(minutes, 'minutes')
        .format('LTS');

I think you missed a key point in the documentation for .add()

Mutates the original moment by adding time.

You appear to be treating it as a function that returns the immutable result. Easy mistake to make. :)

If you use the return value, it is the same actual object as the one you started with. It's just returned as a convenience for method chaining.

You can work around this behavior by cloning the moment, as described here.

Also, you cannot just use == to test. You could format each moment to the same output and compare those, or you could just use the .isSame() method.

Your code is now:

var timestring1 = "2013-05-09T00:00:00Z";
var timestring2 = "2013-05-09T02:00:00Z";
var startdate = moment(timestring1);
var expected_enddate = moment(timestring2);
var returned_endate = moment(startdate).add(2, 'hours');  // see the cloning?
returned_endate.isSame(expected_enddate)  // true

format returns a string, you have to use add on moment object.

Your code could be like the following:

var hours = randomIntFromInterval(0,23);
var minutes = randomIntFromInterval(0,59);
var time = moment(hours+':'+minutes,'HH:mm');
time.add(7,'m');
console.log(time.format("HH:mm"));

Note that you can create a moment object using moment(Object) method instead of parsing a string, in your case:

moment({hours: hours, minutes: minutes});

As the docs says:

Omitted units default to 0 or the current date, month, and year

First of all you need to parse the string data, we know we're using a valid hour.

const time = '15:30' // Valid date
const time = '252:10' // Invalid date

You can use a second parameter in the moment function, something like this:

moment(time, "HH:mm");

You simply need to know what format to convert your string to, read more about that in this documentation link.

Then, you can occupy the different builders to get the expected result.

moment(time, "HH:mm") // Parse the string
  .add(40, 'minutes') // Add 40 minutes
  .add(2, 'hours') // Add 2 hours
  .format('HH:mm') // Format to specified format

And finally you will get your date time parsed.

Here is a working version of this:

const time = '15:30'
const date = moment(time, "HH:mm").toDate();

const parsedDate = moment(date)
  .add(40, 'minutes')
  .add(2, 'hours')
  .format('HH:mm')

console.log(parsedDate);

<script src="https://cdnjs.cloudflare.com/ajax/libs/moment.js/2.29.4/moment.min.js"></script>

var firstTrainTime = 12:00 //input as **hours:minutes**
var frequency = 30         //input as any number (user could for instance enter 1345 minutes) of **minutes**

moment(firstTrainTime, 'HH:mm').add(frequency, 'minutes').format("HH:mm")
//"12:30"

Documentation on #add() for moment: https://momentjs.com/docs/#/manipulating/add/