As I supposed, this option is already included in Lubuntu for users: fortunately, no files of the system have to be modified and no Terminal command lines are necessary to do this editing.

I found the way by myself after some trial and error. Only then I saw that it is (obviously) also precisely described on the official Lubuntu manual page, here.

1. First, find a good icon image you like for your Lubuntu panel and
   save it in your local drive.



2. Then, just go on the panel and right-click on it.

   
   
   

   




3. Click on Configure Panel.




4. Go to Widgets bar.

   
   
   

   




5. Click on Menu or Application Menu (it depends on your Lubuntu
   version).




6. Here a new window appears, showing the path of the image file used
   as the menu icon. If you like, you can back up the default path by
   saving it on a .txt file or as a screenshot, for any problems may
   occur or just to recover default settings.

   
   
   

   




7. Now just type the new path for the main menu icon, corresponding to the path of the image you previously saved.