> Is there any way of identifying whether or not my visitors are using
> one of these plugin?

Yes.

Users can install LastPass as a browser plugin. Thus you can rely on client side scripting languages to check if LastPass is installed. 

For instance, using [`NavigatorPlugins.plugins`][1] allows you to get the  a [`PluginArray`][2] object, listing the plugins installed in the application:


    function getLastPassVersion() {
      var lastpass = navigator.plugins['LastPass'];
      if (lastpass === undefined) {
        // LastPass is not present
        return undefined;
      }
      return lastpass.version;
    }


Note also that what you are asking for is commonly implemented and used by [browser fingerprinting][3] technologies.


> and how best to support it?

Avoid `GET` and use `POST` instead. Example:

     <form action="https://example.com/login.php" method="post">    
         <input type="text" name="username" id="username" value=""/>
         <input type="password" name="password" id="pwd" value=""/>
         <input type="submit" value="Sign in"/>
     </form>

  [1]: https://developer.mozilla.org/en-US/docs/Web/API/NavigatorPlugins/plugins
  [2]: https://developer.mozilla.org/en-US/docs/Web/API/PluginArray
  [3]: https://panopticlick.eff.org/