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If the rotary engine's speed was, say 1200rpm (20 rps), that means that the gun is fired 20 times per second. If it rotates through 360° in 1/20s, it completes 1 revolution in 50ms, which is a pretty short time between rounds being fired.
I also thought that only firing once per revolution may be to allow the gun to cool between firing?
Lastly, I note that the firing sequence happens very soon after the propeller blade passes in front of the gun, I wonder if that was to minimise the risk of powder residue muzzle flash damage on the upcoming propeller blade?
as for the lag you mentioned.... perhaps it reckoned upon the time period between the lever being depressed and the bullet finally reaching the intersection point?