To give a theological answer, no. A lich is usually understood as a sorcerer who has achieved an undead state or immortality, usually by binding their soul to the corporeal world in a phylactery. That does not apply in Jesus' case, since he did not pursue any sort of magic to avoid death, much less binding his soul to a phylactery. The resurrection of Jesus was a supernatural act of God, restoring Jesus to true life.
As to the second part of your question, I was not aware that holy water harming liches was a common trope in fiction (it is usually seen in reference to vampires), but even if it is applied to undead more widely, we have established that Jesus was restored to true life, not to any form of unnatural undeath. Moreover, holiness comes from God (that which is holy is set apart for God), and Jesus is fully God, so contact with holy things would not harm him. Indeed, Christ is now in the true holy place in heaven (Hebrews 9:24), which we can only enter when cleansed by his blood (Hebrews 10:19-22).
You put way too much work into that answer, good for you.
I was going to but he beat me to it. If he resurrected then I would go with the zombie thing because obviously there is no god, but obviously no such resurrection happened so in reality the figure may be person but also may be made up or a collection from several peoples lives or such.
His soul was not bound into a phylactery. You could argue that He was a revenant, but the real answer is that He is a god, who briefly wore a mortal body around one aspect of His godhead (per Christian mythology).
You will always have issues with these sort of crossovers. Mixing characters from two different universes never really works as the rule sets always have conflicts.
You may as well ask if a Jedi would be able to resist turning into a Borg.
If he was that would mean he only ascended to Heaven because someone destroyed his phylactery.
Although there is no explicit evidence in the Gospels, we have reason to suggest that he also may have worn phylacteries.
