It is a physical impossibility for a boltgun to be operated as quickly as a lever. Period. No amount of wishful thinking will ever change that. Ever.
Actually the military considered leverguns a little over 100 years ago and found that with proper training there was almost no difference and under battlefield conditions the bolt gun was considerably faster. Think firing prone.
Got a challenge for you. I'm going to the range in the AM if it isn't raining too hard. Taking a Marlin 30-30, 44 mag, and a Winchester 308 along with a stop watch and someone to time me. Going to fire 3 rounds from each rifle just for pure speed, no target.
Next I'm going to put up a 9" paper plate at 50 yards and repeat, but all 3 shots must hit the plate. I use this drill quite often for practice, but have never timed myself. Never noted any real difference in time either. One of the levers may win, but I seriously doubt there will be 1/2 second between 1st and 3rd place. Especially if anyone actually has to aim and hit something. Either action type can be cycled faster than you can get the sights back on target. I actually think the bolt gun will have an advangtage with the target because the better stock design and optics make it easier to get on target quicker.
Here is why. On my 30-30 the lever throw is 9" out, 9" back. The 44 is 6.5" out, 6.5" back. On the 308 the bolt throw is only 4.25" back, 4.25" forward. I do have to lift and lower the bolt handle, but the human body is capable of moving 2 body parts at the same time. i can roll my wrist to lift and lower the bolt at the same time my arm is moving back and forward.
Also on the lever you must overcome a lot more resistance to moving the lever than with a bolt.
I'll report back tomorrow, If I don't get rained out. If I can't get to the range tomorrow it might be next Tuesday before I'll have another chance.