link on the same page inside lightbox

can you give to that link the class: popup-modal-dismiss and see if that is enough to do

the function on magnific popup doku to close the popup is: $.magnificPopup.close();
may i see your function of the popup?

is it an inline popup or how did you get the anchor link into the popup – please post it here:

this could be a function that will do the job – you can choose any trigger class for it you like

  $(document).on('click', '.popup-modal-dismiss', function (e) {  
    $.magnificPopup.close();
  });

this could be part of your inline-popup script or an extra snippet – easier to give advice if i see your code.

look here : https://kriesi.at/support/topic/graceful-transition-for-pop-up-modals/#post-1205887