Lucian Adjust?

I believe that a really cool idea for Lucian would be if is ultimate bullets would also tick down the cooldown on his E like his auto attacks do. Of course this would be a pretty strong buff to the already strong champion but it could add a better sense of reward and a new gameplay mechanic to Lucian' kit. It could be balanced with any combonations of these changes. 1 E cooldown up 2 Less R shots but damage up to keep damage 3 Only apply to champion hits or only minion bits