Lich bane: life steal off the 75% physcial damage?

So i was thinking one way to buff akali or kata now that dfg is gone would be to give lichbane's sheen proc some life steal. This is such a minor buff its laughable. we're talking peanuts of a difference. But still a buff no less. The reason I think this would work is because lichbane is like to only other item aside from dfg that gave you extra burst aside from your kit. Lich bane would pair very well with gunblade imo.

The following is a post i made a while back in the now archived boards Lich bane: life steal off the 75% physcial damage?Source

Would be nice if this could be tested out in pbe. I'd like to try it on jax with rageblade. I think it would be balanced since you have to itemize for lifesteal which would take up slot making you more bruiser oriented. granted rageblade is nice in that it can provide for the ap as well. but the lifesteal is only obtained at risky health levels.

It'd be kind of like nidalee q it does magic damage but can still lifesteal. i dont see it being game breaking since without much magic pen ull lifesteal less from lb and with magic pen items you sacrifice ad.