You need to append that link just as link with no parameters, then you need to create a click
function with the parameters like:
$('#allList').append('<li><a id="SOME_ID">'+ allDeadline.class +'<br>'+ allDeadline.duedate+' '+ allDeadline.duetime+'<br>'+ allDeadline.description +'</a></li>');
$(document).on("click", "#SOME_ID", function(){
// do your stuff with parameters
});