jQuery .ajax(): asynchronous with return vs. synchronous with callbacks

Question

I have some code that uses .ajax() to query a MySQL database to return some data which is then used by JavaScript code to "do stuff." Currently, my AJAX calls are set to "async : false," which makes the call "synchronous." I'd like some advice on how to change these synchronous calls to work asynchronously using callbacks by way of the .done() function, etc.

I will paste some code snippets that hopefully will show enough of what happens currently:

function lkup(data) {
  param = data;
  var tbl = param.tbl;
  var sdate = param.sdate;
  var called_by = param.called_by;
  var hn2_event = param.hn2_event;

  var field_id          = param.field_id;
  var code              = param.code;
  var field_to_populate = param.field_to_populate;
  screen_data           = param.screen_data;

  var os_data  = screen_data.os_data;
  var osdc     = screen_data.osdc;
  var os_dmid  = screen_data.os_dmid;
  var os_dtnid = screen_data.os_dtnid;
  var os_dln   = screen_data.os_dln;
  var os_dlnt  = screen_data.os_dlnt;
  var os_icode = screen_data.os_inv_code;
  var os_dfid  = screen_data.os_dfid;
  var os_adj   = screen_data.os_adj;

  // Get the reco number for this reco:
  var split_array = field_id.split("_n_");
  var reco_number = split_array[1];
  // Rebuild field_id:
  field_id = split_array[0] + '_n_' + reco_number;

  // Get various drug_tbl information for this code:
  var drug_record_info='';
  var drug_type='';
  var ndc_needed='';
  var disp_unit='';

  // If this is a blank drug code, the user cleared out the drug.  Do NOT try to get drug type:
  if ( osdc == "" && (dc.test(field_id) || vx.test(field_id)) ) {
     // do nothing
  } else if (ic.test(field_id)) {
     // do nothing
  } else {
     drug_record_info = getDrugType(osdc,drug_record_info);
     var drug_info_array = drug_record_info.split("|");
     drug_type  = drug_info_array[0];
     ndc_needed = drug_info_array[1];
     disp_unit  = drug_info_array[2];
  }

  // If the code was blank (''), clear the appropriate display-only fields:
  // TODO: First, we have to figure out WHICH field is being populated; then, we need to handle clearing
  // display-only fields
  if (code == "") {
     clear_dose_amount(reco_number, drug_type, ndc_needed);
     clear_qty_on_hand(reco_number, drug_type, ndc_needed);
     clear_unit_display(reco_number, tbl);
     clear_dosage_form_id(reco_number);
  }

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In the snippet above, I'm interested in how to change the call to getDrugType so that it uses a callback function. Here's the getDrugType function:

//function getDrugType(code, drug_record_info) {
function getDrugType(code, drug_record_info) {

 // Don't lookup anything if code is 'blank' or '':
  if (code == '') {
     return;
  }

  $.ajax({
           type      : "POST",
           url       : "HNJQUERYBRIDGE.pl",
           cache     : false,
           async     : false, // I need the javascript to wait for this function to complete!
           data      : {
                             dbase : param.dbase,
                              code : code,
                           session : param.session_id,
                             event : 'lookup_drug_type',
           },
           dataType  : "text",
           error     : networkErrorMessage,
           success   : function(data) {
                          drug_record_info = setDrugType(data, drug_record_info);
                       },
    });

    return(drug_record_info);

}; // getDrugType()

 //function setDrugType(data, drug_record_info) {
 function setDrugType(data, drug_record_info) {
   drug_record_info=data;
   return(drug_record_info);
};

The data returned as "drug_record_info" is an array, which is used in various places throughout the rest of the JavaScript code as "drug_type" and "ndc_needed", etc.

If this code doesn't make sense I'll try to explain in more detail if necessary.

I appreciate any help!