Class to interact with cookies
As Dvorak said in the comments, your code is fine as-is. Still, I have some suggestions:


I'd forego the *Cookie suffix on the function names. Seems too verbose, considering the constructor is called Cookies already. Only trick is that you can't have function called delete as that's a reserved word, but remove works fine too.
I think you have a bug: In deleteCookie you call your own setCookie with a negative lifetime - but setCookie doesn't take a lifetime argument, so the cookie won't be deleted as expected.
I'd fix this by adding such a 3rd argument to setCookie but making it optional:

function setCookie(name, value, lifetime) {
  var date, expires = '';
  // default to cookieLifeTime if no arg was passed
  if( typeof lifetime !== 'undefined' ) {
    lifetime = cookieLifeTime);
  }
  if( lifetime ) {
    date = new Date();
    date.setTime(date.getTime() + lifetime);
    expires = '; expires=' + date.toGMTString()
  }    
  document.cookie = name + '=' + value + expires + '; path=/';
}

The getCookie can be made considerably shorter with a bit or regular expression magic.

function getCookie(name) {
  var pattern = new RegExp(name + '=([^;]+)', ''),
      match = document.cookie.match(pattern);
  if(match) {
    return match[1];
  }
  return null;
}

As RoToRa says in another answer, a simple object literal might be neater, if you're willing to either skip the cookieLifeTime instance variable, or make it completely global. Here's how I'd probably write it:

// lowercase, as it's no longer a constructor
window.cookies = {
  set: function (name, value, lifetime) {
    var date, expires = '';
    // for mysterious reasons `NaN` is a number in JS,
    // so check for NaN too
    if( typeof lifetime === 'number' &amp;&amp; !isNaN(lifetime) ) {
      date = new Date();
      date.setTime(date.getTime() + lifetime);
      expires = '; expires=' + date.toGMTString()
    }    
    document.cookies = name + '=' + value + expires + '; path=/';
  },

  get: function (name) {
    var pattern = new RegExp(name + '=([^;]+)', ''),
        match = document.cookie.match(pattern);
    if(match) {
      return match[1];
    }
    return null;
  },

  remove: function(name) {
    window.cookies.setCookie(name, '', -1);
  }
};