Take a look of my code I did for a Customer and see if this could give you hint to fix yours

 $('#q152 input').change(function () {
        if ($('#q152 input[value="Manual"]:checked').length > 0) {
            $('#q125').hide();
            $('.AccountInfo input').removeAttr('readonly');
            if (!$('.FieldReq input').prop('required')) {
                $('.FieldReq label, .FieldReq2 label').append('<span class="cf-required">*</span>');
                $('.FieldReq input,.FieldReq2 input').attr('required', 'True');
                //$('.FieldReq2 label').append('<span class="cf-required">*</span>');
                // $('.FieldReq2 input').attr('required', 'True');
            }
            $('.OrderInfo input').removeAttr('readonly');
            $('.Submit').removeAttr('disabled');
            $('#q126').hide();
        } else {
            $('#q125').show();
            $('.AccountInfo input').attr('readonly', 'True');
            $('.FieldReq span.cf-required').remove();
            $('.FieldReq input').removeClass('required').removeAttr('required');
      $('.FieldReq2 span.cf-required').remove();
            $('.FieldReq2 input').removeClass('required').removeAttr('required');
            $('.OrderInfo input').attr('readonly', 'True');
            $('.Submit').attr('disabled', 'disabled');
        }

Thank you for the responses.  I appreciate it.  After reviewing Rene's code, I have tweaked mine a little.  However, it is still allowing a form submit without an entry in the Driver drop-down - even when it should be required.  The radio button defaults to Employee so the Driver drop-down should be set to required upon form load.  Anytime the radio button is changed, the Driver drop-down required attribute should be updated accordingly.

As a follow up and closure to this question...Per Junald's suggestion, I was able to mark the field as Required on the form and set up Field Rules to Show/Hide the fields based on the value of the Radio Button.  (Hiding/Showing the field using Javascript had no effect on the Required indicator.  The result being that if the field was hidden, an entry was still required.)  Using Field Rules allowed for the field to be Hidden and not Required OR Shown and Required.

Validate field as required or optional using field rules is supported in new form designer with Forms 11 Update 3.

You can see other changes of Forms 11 Update 3 from  https://support.laserfiche.com/kb/1014413/list-of-changes-for-laserfiche-forms-11-update-3 and get Forms 11 Update 3 from Laserfiche 11 package  https://support.laserfiche.com/kb/1014263/software-versions-and-fixes-included-in-the-laserfiche-11-download-package.