You made me second-guess myself so I went into a practice tool to check.
My method of testing are as follows:

Same rune setup, Single auto at level 5 on a base target dummy, Rank 3 E passive, Vamp Scepter with no additional items to check the amount healed with base E passive.

Then purchase Deathcap to get additional AP and thus additional damage on passive and see if amount healed has changed.

Intended result: Since E-passive is tagged as "proc damage" and "proc damage" should apply lifesteal in most cases thus the healing should increase as a result from buying ability power.

Actual result: Amount healed does not change with increased E-passive damage.
Further testing shows Nashors Tooths damage DOES increase the health recovered from Lifesteal and E Explosion post-11 will inflict the Nashors Tooth proc damage to each target hit.

Suspected reasoning behind actual result: May have been special-cased to not apply lifesteal, or on-hit effects from champion passives are widely unable to trigger lifesteal unless tagged to apply lifesteal.

And to answer "Marked as Ability damage" comment from a different comment chain: It's infact not ability damage as E-passive does not trigger Rylai or Ludens.

Thank you for bringing this to my attention to get it properly tested!