If 7 > 51 of 9999 > 15000 is evaluating as true, that's a big flag that it is comparing the values as strings instead of numbers.  It's basically saying that alphabetically, 7 comes after 5 and 9 comes after 1 - both true, but not helpful in this situation.

Try converting your values to numbers, like this with the parseFloat function: 

    var iValue = parseFloat($('.IValue input').val());
    var aLimit = parseFloat($('.ALimit input').val());

Another note, I think you should probably use a document ready codeblock instead of document change, so that it runs on the form load, but not every time a change happens on the form.

Regarding it not doing the validation when the lookup is complete, we can trigger it to run some code when the lookup is complete (document onloadlookupfinished block and a document lookupcomplete block).  The following code will trigger every time that the lookups complete (we can make it more specific by referencing the event value, but running it on the completion of any lookups may work for your purposes).  Within those code blocks, we'll run the validation on the specific fields.  In order for that to work, when you are adding the validation element to the fields we also need to add a validation group (like this: attr('data-parsley-group','IValueAndALimit')), so that we can call that specific group late on.  Put it all together and it should look something like this: 

$(document).ready(function () { 

  // custom validator for name confirmation
  window.Parsley.addValidator('samevalue', 
  {
    validateString: function(value, requirement, field) 
    {
      var iValue = parseFloat($('.IValue input').val());
      var aLimit = parseFloat($('.ALimit input').val());
    
      return (iValue <= aLimit || iValue == '' || aLimit == '');
    },
    messages: 
    {
      en: 'Approver Limit Cannot Be Smaller Than The Invoice Value!.',
    }
  });
  // assign validator to name fields
  $('.IValue input, .ALimit input').attr('data-parsley-samevalue','').attr('data-parsley-group','IValueAndALimit');
});

$(document).on("onloadlookupfinished", function (event) {
  $('#form1').parsley().validate('IValueAndALimit');
});

$(document).on("lookupcomplete", function (event) {
  $('#form1').parsley().validate('IValueAndALimit');
});