Converted CSS/HTML theme to D7, .js files ignores integrated jQuery and works only with jQuery imported via .info
add a anther js file via theme's .info;

scripts[] = js/mycustomscript.js


dont add your inline script in html.tpl.php , add it in mycustomscript.js file like

(function ($) {

  Drupal.behaviors.exampletheme = {
    attach: function (context, settings) {
      $(".carousel").jCarouselLite({
                btnNext: ".next",
                btnPrev: ".prev"
     });
    }
  };

})(jQuery);