// add parser through the tablesorter addParser method
$(function(){

  $.tablesorter.addParser({
    // set a unique id
    id: 'data',
    is: function(s) {
      // return false so this parser is not auto detected
      return false;
    },
    format: function(s, table, cell, cellIndex) {
      var $cell = $(cell);
      // I could have used $(cell).data(), then we get back an object which contains both
      // data-lastname & data-date; but I wanted to make this demo a bit more straight-forward
      // and easier to understand.

      // first column (zero-based index) has lastname data attribute
      if (cellIndex === 0) {
        // returns lastname data-attribute, or cell text (s) if it doesn't exist
        return $cell.attr('data-lastname') || s;

      // third column has date data attribute
      } else if (cellIndex === 2) {
        // return "mm-dd" that way we don't need to use "new Date()" to process it
        return $cell.attr('data-date') || s;
      }

      // return cell text, just in case
      return s;
    },
    // set type, either numeric or text
    type: 'text'
  });

  $('table').tablesorter({
    theme: 'blue',
    headers: {
      0 : { sorter: 'data' },
      2 : { sorter: 'data' }
    },
    widgets: ['zebra']
  });

});

<table>
<thead>
  <tr>
    <th>Name (Last)</th>
    <th>Originally from...</th>
    <th>Birthday</th>
  </tr>
</thead>
  <tbody>
    <tr>
      <td data-lastname="Allen">Joe Allen</td>
      <td>South Carolina</td>
      <td data-date="01-15">Jan 15</td>
    </tr>
    <tr>
      <td data-lastname="Torres">Lisa Torres</td>
      <td>Maryland</td>
      <td data-date="03-02">March 2nd</td> <!-- leading zeros needed to sort properly! -->
    </tr>
    <tr>
      <td data-lastname="Franklin">Peter Louis Franklin</td>
      <td>Coventry</td>
      <td data-date="12-26">Boxing Day (Dec 26th)</td>
    </tr>
    <tr>
      <td data-lastname="Jones">Maria Consuela de Los Angeles Ortiz Del Toro-Jones</td>
      <td>Texas</td>
      <td data-date="05-10">10 Mayo</td>
    </tr>
    <tr>
      <td data-lastname="Bigglesworth">Mike "the Smasher" Bigglesworth</td>
      <td>Rhode Island</td>
      <td data-date="06-22">22nd of June</td>
    </tr>
    <tr>
      <td data-lastname="Smith">Fredrick Smith</td>
      <td>Ohio</td>
      <td data-date="03-10">10th Mar</td>
    </tr>
  </tbody>
</table>