There are probably better ways to select the proper map layer node but this should work
Code:
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
  
  <xsl:template match="/">
    <table border='1' width='100%'>
      <col width="15%" />
      <col width="35%" />
      <col width="15%" />
      <col width="35%" />
      <xsl:for-each select ='NewDataSet/FACILITY_INFO'>
        <tr>
          <td>Facility Number</td>
          <td>
            <xsl:value-of select='FACILITY_NUMBER'/>
          </td>
          <td>Layer Name</td>
          <td>
            <xsl:call-template name='maplayer'>
              <xsl:with-param name='layerId'>
                <xsl:value-of select ='LAYER_ID'/>
              </xsl:with-param>
            </xsl:call-template>
          </td>
        </tr>
        <tr>
          <td>Description</td>
          <td>
            <xsl:value-of select='FACILITY_DESC'/>
          </td>
          <td>Facility ID</td>
          <td>
            <xsl:value-of select ='SDS_ID'/>
          </td>
        </tr>
      </xsl:for-each>
    </table>    
  </xsl:template>
    
    
  <xsl:template name='maplayer'>
    <xsl:param name='layerId' />
    <xsl:for-each select='//MAP_LAYER'>
      <xsl:if test='LAYER_ID = $layerId'>
        <xsl:value-of select ='LAYER_NAME' />
      </xsl:if>
    </xsl:for-each>
  </xsl:template>
  
</xsl:stylesheet>