No, you can't push a Lightning-Immune Creature using the Thunderbolt Strike Feature.
As I read the feature and understand the mechanics, an immune creature cannot take damage from whatever it is immune to. Therefore, effects which depend on damage cannot take place against said creatures.
I think this would be a fine interpretation if the description read "when you hit a creature with a spell that deals Lightning Damage", because there's no requirement in that description that actually requires the creature to take damage, but here, I don't think that's the case.
The alternative reading is to infer that Immune Creatures "reduce damage by 100%", implying that the creature takes "0 damage", and thus still qualifies. But I think that's a weird reading, and I think my overall conclusion, that immune creatures do not trigger "when damaged" effects, stands. My interpretation is also supported by Crawford, who asserted that taking 0 damage means taking no damage, and specifically used this feature as an example of an effect that would not trigger on a creature immune to the damage type.