Is it a twin spark or a single spark variant ? Could be its got a duff main coil (But they "usually" fail when you are on acceleration!)
Fuel pump "Usually" fails at higher RPM or just does not work! Even if a pipe is split it "usually" can create enough pressure for tickover.
Was the the fault present before you went into the tank or after ??
Does it idle like that all the time? Or just when it is about to conk out?
Were you in standing traffic and the bike over 5 bars on Temp gauge?
Was it wet ?? Any difference between wet and dry conditions?
Did the revcounter flick about all over the place?
Also re Lambda Just unplug it from loom, I have seen about 5 where even a new Lambda does not cure the issue and unplugging it does Perhaps a loom fault (or a faulty new part But I get NGK from a local autofactor so a trusted source!) The ECU defaults to a base map so will run okay in fact I know a few have been disconnected for a LONG time
You can slip the black front cover down and out the left side and examine the HES wiring for cracks or damage
I would diagnose stuff more thoroughly before pulling the trigger on the parts cannon and wonder what the heck cured it
Edit extra thoughts ...................Was the bike up to working temperature??? If it was cold and you do not have the throttle cracked open, it's way too rich and will stall and likely start straight back up
Have you checked the TPS settings? .38 volt with Ign on
Have you the idle set to 1050 rpm + or - 50rpm When at 5 bars