Does the Blade of the Ruined King's Passive On Hit Effect Proc Lifesteal?

IF this were the case, Talon/Riven would have absurd reason to build Lifesteal. He and she do not regain life by spamming skills.

Lifesteal applies to the physical damage done by base attacks. (This includes AA resets like Talon's Noxian Diplomacy, Nasus' Siphoning Strike, Darius' Crippling Strike, Draven's Spinning Axe)

Spell Vamp applies to damage dealt by abilities, regardless of the damage type. (This includes AA modifiers like Sivir's Ricochet, Kha'Zix's Unseen Threat, Jax's Grandmaster's Might and Empower, Irelia's Hiten Style true damage, Poppy's Devastating Strike, Nidalee's Takedown)