It doesn't do physical damage.
Life steal is based on auto-attacks just like Thornmail, Tabi, and Doran's Shield though.
Champions like Warwick and Poppy do actually life-steal with magic damage auto-attacks.
There's something called Spell Vamp, which is the same as Life Steal only it works for your magic based abilities.
Spell vamp doesn't care what type of damage an ability does.
It just works with all abilities.
Darius's true damage? Smite's true damage? Riven's physical damage? Zed's physical damage? Garen's Spin to Win? Pantheon's Spear? Yi's Alpha Strike? Spell vamp doesn't care - it only cares you're using a spell.
Unless that "spell" is an on-hit effect, a Sheen-like auto-attack booster, or an ability masquerading as an auto-attack that applies on-hit effects (Mystic Shot, Blade Waltz, Infinite Duress, Double-Up, Twin Bite, Parrrley, 3-Talon Strike, Tumble, Siphoning Strike, etc.) Outside of on-hit effects, those all apply life steal though.