Whether or not you go with a knock off or authentic Weber, read through the thread I am linking for some really helpful information regarding installation and setting up. In the thread there is a video I posted that is really informative and thorough for tuning. Also, keep the throttle cable linkage from the Hitachi to install on the Weber and save yourself a lot of headache by looking into the one piece adapter I mention in the thread. Since you have a L20 you would need a low profile air filter for the Weber.
Here is a picture of the Hitachi throttle cable linkage on the Weber
One piece adapter installed