Is there a way a plugin can watch for live preview updates?
You will probably have to use javascript. Something like this would work.

$('.lp-iframe').on('load', function(event) {
  console.log(event);
});


edit

Try this to bind the lp-iframe after it gets added to the page. 

$('.livepreviewbtn').on('click', bindIframe);

function bindIframe() {
  $('.livepreviewbtn').off('click', bindIframe);
  $('.lp-iframe').on('load', function(event) {
    console.log(event);
  });
}