You can try this approach.. (if only you've direct text node in your div)
window.getSelection().focusNode.parentElement //returns the selected element
so you can set attr like
window.getSelection().focusNode.parentElement.setAttribute('data-id', 'id-1');
You can wrap it in a 'mouseup' event with your current div
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>Document</title>
</head>
<body>
<div id="myDiv">
Lorem ipsum dolor sit amet, consectetur adipisicing elit. Id natus voluptatibus eum explicabo soluta excepturi?
</div>
<div id="myDiv2">
Lorem ipsum dolor sit amet, consectetur adipisicing elit. Id natus voluptatibus eum explicabo soluta excepturi?
</div>
<script>
var myDiv = document.getElementById('myDiv')
myDiv.addEventListener('mouseup', function(){
window.getSelection().focusNode.parentElement.setAttribute('data-id', 'id-1');
})
</script>
</body>
</html>
Or it is best approach to add attr to selected 'div' only, if there is many divs
var div = document.querySelectorAll('div')
for(var i = 0; i < div.length; i++){
div[i].addEventListener('mouseup', function(){
window.getSelection().focusNode.parentElement.setAttribute('data-id', 'id-1');
}, false)
}