What an interesting question.

Under RAW, it would not heal. Spell Secrets is pretty specific that only the damage type is substituted, and furthermore, at least for the wording under Vampiric Touch the healing specifically comes from necrotic damage dealt.

Make a melee spell attack against a creature within your reach. On a hit, the target takes 3d6 necrotic damage, and you regain hit points equal to half the amount of necrotic damage dealt. Until the spell ends, you can make the attack again on each of your turns as an action.

Technically there was no necrotic damage dealt here. And that makes sense. Why would fire damage heal the caster like siphoned off necrotic energies.

That said, RAI, it would not be the end of the world to extend the healing to this power.

NOTE: Unearthed Arcana is playtesting material, and may not be balanced, worded well, or workable.

110 feet

Jeremy Crawford confirmed that each magic missile dart is a separate instance of damage, at least in the context of concentration:

@JeremyECrawford Do you roll concentration for every instance of damage taken? id est every Magic Missile hit?

Concentration: "You make a separate saving throw for each source of damage" (PH, 203). Roll for each missile. #DnD

Barring anything that explicitly says that concentration is a special case that treats magic missile differently than other things (or that thunderbolt strike is such a special case), the only possible consistent interpretation is that each dart from magic missile is a separate source of damage. When you make it lightning damage, then you deal a separate instance of lightning damage for each one. Which means that, for each one, “when you deal lightning damage” is triggered.

The fact that magic missile darts deal their damage “simultaneously” is absolutely irrelevant: thunderbolt strike makes no reference to time in its wording. It only says “when you deal lightning damage.” So you roll the first dart’s lightning damage, and that point in the resolution of your turn is a point “when you [did] lightning damage,” so you push the target back 10 feet—and then you move on to resolve the next dart.

There is absolutely no basis in the rules or in developer commentary, that I have seen, that justifies treating them as a single instance of lightning damage for the purposes of thunderbolt strike, despite them being separate sources of damage for concentration. That is an inconsistent interpretation that would require special exceptions to the rules to justify, and no such special exceptions are written anywhere (to my knowledge).