League-of-legends – Do the hits from Lulu’s passive (Pix) proc on-hit effects or count for number of hits

Life Steal and Spell Vamp don't proc based on the damage bonus source of the skill (AD versus AP), nor is it based on the damage type (physical versus magical). It's actually based on the kind of skill.

In general, Spell Vamp is the only drain effect that affects skills. All of Lee Sin's skills, despite all being AD-based physical attacks, use Spell Vamp and Spell Vamp alone. Akali is an example of a somewhat physical champion whose attack skills are all Spell Vamp-based (her innate Life Steal is to benefit her auto-attacks only). Even skills like Ashe's Volley, which applies her Frost Shot effect (but only that, the key point being as you'll read up soon), will use Spell Vamp.

Life Steal generally applies only to your auto-attack, but it also applies to skills that apply on-hit effects. For example, Blitzcrank's Power Fist deals 100% extra damage and pops the target in the air in addition to applying on-hit effects (for items like Black Cleaver). This benefits from Life Steal instead of Spell Vamp. Other examples of skills that benefit from Life Steal would be Irelia's Bladesurge, Ezreal's Mystic Shot, and Gangplank's Parrrley.

As far as I know, there is no skill which benefits from both Spell Vamp and Life Steal. It's always one or the other.

The Spell Vamp portion of the LoL Wiki and my own experience show that

[Spell Vamp] works off of activated item effects, summoner spells, and abilities, regardless of the type of damage done.

Therefore, items that give proc effects to attacks like Bloodrazor, Wit's End, Malady, Wriggles etc, will NOT grant the user health through spell vamp.

On a side note, Ezreal's Mystic Shot (Q) applies on hit effects, including but not limited to, lifesteal.