No lever on the pump.
If it's a Weber DGAV, these are notorious for 'drying out' Like yours, if i use mine daily, she catches straight away. If I use her weekly, it take a fair bit of priming before she'll start. However, you seem to be doing all the right checks.
Often, if I'm restarting bikes from a long lay up (months), I'll give a little squirt of 'easy start' just to get things going and everything pumping nicely. That will also let you know if the ignition system is working properly and fuel is pumping, People frown, but far less strain on battery and start motor.
Possible causes and solutions.
a)sediment has formed and settled in the tank blocking the pickup. If you fancy, you can blow the pipe, but be prepared for serious 'blow back'. An airline would be best (or even a can of compressed air). I'd also blow down into the fuel fuller and see if any fuel is coming out the pipe. Again, same warning about blow back.
b) Pump has failed/blocked - remove top and check diaphragm/filter guaze. If it runs on Easy Start, and the tank/pipe is unblocked then there's your issue. You could also set up a gravity feed tank to see if that works,
