Fine, keep the cooldown, make it a guaranteed proc like Mystic Shot.Lucky shot had a multiplicative effect, meaning it doesn't matter how fast you are shooting or how strong your bullets are, lucky shot affects your damage the same way.
Tesla bullets add flat damage. So no, Tesla bullets cannot work the same way as lucky shot, it needs a cooldown.
Or, if we want to remove the cooldown, we can make it a chance proc and scale the damage to FR (like Silencer and Spiritual Overflow). Lowering the damage to counter increased or guaranteed procs is an easy fix.
Either way, keeping both is overkill.