There is:

SHtml.text... 
SHtml.ajaxText... 
SHtml.textarea..

but no

SHtml.ajaxTextarea...

Background discussion: http://groups.google.com/group/liftweb/browse_thread/thread/d538728a21e78aa9/d841a33d7ddb8420#d841a33d7ddb8420

I was able to work around this problem from simply copying the SHtml.ajaxText code and changing it to use textarea tags and commenting out the submit on CR line:

object SHtmlExtension {
	import net.liftweb.http.js.{ JsCmd, JsExp }
	import net.liftweb.http.js.JsCmds._
	import net.liftweb.http.js.JE.{ AnonFunc, Call, JsRaw }
	import net.liftweb.http.S.{ contextFuncBuilder, fmapFunc, formFuncName, AFuncHolder, SFuncHolder }

  def ajaxTextarea(value: String, func: String => JsCmd, attrs: (String, String)*): Elem = 
  ajaxTextarea_*(value, false, Empty, SFuncHolder(func), attrs: _*)

  def ajaxTextarea(value: String, jsFunc: Call, func: String => JsCmd, attrs: (String, String)*): Elem = 
  ajaxTextarea_*(value, false, Full(jsFunc), SFuncHolder(func), attrs: _*)

  def ajaxTextarea(value: String, ignoreBlur: Boolean, func: String => JsCmd, attrs: (String, String)*): Elem =
  ajaxTextarea_*(value, ignoreBlur, Empty, SFuncHolder(func), attrs: _*)

  def ajaxTextarea(value: String, ignoreBlur: Boolean, jsFunc: Call, func: String => JsCmd, attrs: (String, String)*): Elem =
  ajaxTextarea_*(value, ignoreBlur, Full(jsFunc), SFuncHolder(func), attrs: _*)

  private def ajaxTextarea_*(value: String, ignoreBlur: Boolean, jsFunc: Box[Call], func: AFuncHolder, attrs: (String, String)*): Elem = {
    val raw = (funcName: String, value: String) => JsRaw("'" + funcName + "=' + encodeURIComponent(" + value + ".value)")
    val key = formFuncName

    fmapFunc(contextFuncBuilder(func)) {
      funcName =>
      (attrs.foldLeft(<textarea>{value}</textarea>)(_ % _)) %
      //("onkeypress" -> """liftUtils.lift_blurIfReturn(event)""") %
      (if (ignoreBlur) scala.xml.Null else
       ("onblur" -> (jsFunc match {
              case Full(f) => JsCrVar(key, JsRaw("this")) & deferCall(raw(funcName, key), f)
              case _       => makeAjaxCall(raw(funcName, "this"))
            })
        ))
    }
  }

	// copied from SHtml because it is private there
  private def deferCall(data: JsExp, jsFunc: Call): Call =
    Call(jsFunc.function, (jsFunc.params ++ List(AnonFunc(makeAjaxCall(data)))): _*)

}

thank you