Zimone and Dina

Whenever you draw your second card each turn, target opponent loses 2 life and you gain 2 life.
{T}, Sacrifice another creature: Draw a card. You may put a land card from your hand onto the battlefield tapped. If you control eight or more lands, repeat this process once.

March of the Machine

March of the Machine Promos

For the activated ability, repeating the process means the entire effect, but not the cost. You don’t have to (and, in fact, can’t) sacrifice another creature. You’ll draw another card, then you may put another land card from your hand onto the battlefield tapped. As this is your second time through the process, the ability will finish resolving.

Zimone and Dina doesn’t need to have been under your control when the first card is drawn for its ability to trigger. As long as you control it when you draw your second card in a turn, that ability will trigger.