Modern Vespa

Hello all, first post here!
This forum has already been so helpful! Thank you

I just bought a 2007 bv250 ie and I'm trying to solve an annoying problem... BTW I work on bikes but always with carbs so I'm pretty confident with a spanner...

The bike idles erratically and will sometimes stall.
The bike is running lean. On the overrun I can hear it popping etc.
When pulling away if you open the throttle slowly the bike will die.
When I pulled the plug out it was white.
Everything points to lean running conditions.
Engine light comes on on most rides

I've done the following to try and resolve it...
New, correct spark plug.
HT lead trimmed back and cap reattached
Checked battery and reg rec
Checked air filter
Checked resistance on 4 wire lambda probe
Reset ecu by battery disconnection
Checked and cleaned all electrical connections in engine bay
Sprayed carb cleaner around intake to check for vacuum leaks. Checked all boot connections

The po said that he'd connected an obd2 reader and got errors for the lambda sensor but as I say I have checked the resistance and its OK.
I've tried running with the lambda sensor disconnected and it runs exactly the same.

The po also said they tried taking apart the injector and cleaned it.

I'm in Sydney so there is no evap system

Any ideas on what to try next? New lambda. I really don't know.

Thanks!

Nobody have any thoughts?

Replace the injector. You can get just the injector not the plastic part on top on eBay cheap

Thanks. I've ordered one and I'll try it.

I received the injector and fitted it. Success! Thank you so much!
It's still not 100% correct though. It has a hesitation just as you first open the throttle. This is worse when the engine is cold. This means it's still running lean at that point. Once the throttle is passed the initial small opening it runs great!