MTGNexus

I'm trying to figure out if these can go infinite together?
So say you exile the Leonin Relic-Warder with Temporary Lockdown and then use Aminatou, the Fateshifter to blink the Temporary Lockdown.
I'm not sure how triggers fire off in order?
The alternative is that Temporary Lockdown is play then you exile it with Leonin Relic-Warder and then use a card like Ephemerate to blink it. Will this stack to go infinite as well?

Neither of these combos functions as you wish. You choose the order for the abilities but regardless of the order you choose, it won't grant the results you're after.

In the first, Aminatou blinks the lockdown resulting in both the lockdown and the warder abilities on the stack. If you order the warder first it exiles the lockdown causing its ability to do nothing as its duration is already over. If you go the other way the warder is exiled before its ability resolves. Meaning it tries to return to play the enchantment it exiled but there isn't one so nothing happens then it exiles the Lockdown never to return and returns itself to play exiling another artifact or enchantment.

The second combo is more of the same.