Temporal Rift can't use Lifetap

Having an issue with Temporal rift since I started using Archmage. I use mind over matter so my mana is drained before my HP when I take damage. The way I use this is by using Temporal Rift when I start taking HP Damage to refill my hp and mana. My issue is that with Archmage, Temporal rift now has a mana cost so I can not cast it while I am out of mana and taking hp damage. I feel that this is fair, but my issue is that I am unable to equip the Lifetap passive support gem to Temporal Rift so that I can still cast it without mana.

TLDR; I think Temporal Rift should be able to have the Lifetap support gem because other skills can give it a mana cost, in my case Archmage.