have you checked the advance curve with a stobe ?
If you haven't thoroughly cleaned the carb and jets thoroughly you will definitely need to do so to remove ethanol residues. Some of the jets have holes that are less than 1mm in diameter !
Make sure that you have set the idle, choke and air screw settings correctly or it will always be difficult to start . Its a critical mixture . If your throttle/slide idle setting is too high or too low it will prevent your cold start working as the engine will be getting too much or too little air and or fuel .
Given the uncertain history of the scooter I would recommend that you go through everything cleaning electrical connectors and re-magnetizing the flywheel , new spark plug etc .Replace the HT lead and cap etc
Reliable starting and running is a product of lots of little things all working efficiently together .
To give you an idea ...my 1964 lis150 starts on the second kick every time no matter what the weather , temperature or how long its been left ...even 6 x months over the Winter ! yet as far as I can tell its still on its original 51 year old clapped out engine
