Can you react and kill the targeted unit of Blood Rose Lab before it resolves to still get the card with it from something like a Hidden Hidden Blade at that battlefield?
Yes, you can react to the Dusk Rose Lab ability after it is placed on the chain to kill your own unit, and you can still resolve the lab's ability to draw a card, provided your unit is still present when the lab's ability resolves.
However, there is a nuance: if you kill your own unit using Hidden Blade (or any other effect) in response to the Dusk Rose Lab ability, the unit will be in the trash when the lab's ability resolves. Because the lab requires you to kill a unit you control here as a cost to draw, if that unit is already gone, you cannot pay the cost, and you will not draw the card.
Sequence of Events
- Beginning Phase: The Dusk Rose Lab ability is automatically added to the chain.
- Chain is CLOSED: You now have the opportunity to play [Reaction] cards, such as playing Hidden Blade from hidden.
- Reaction: You play Hidden Blade targeting your unit at that battlefield.
- Chain Resolution:
- The chain resolves Last-In, First-Out (LIFO). Hidden Blade resolves first, killing your unit.
- Next, the Dusk Rose Lab ability attempts to resolve.
- Resolution Outcome: Because the unit is no longer at the battlefield to be killed, you cannot pay the cost required by the Dusk Rose Lab ability. As a result, the ability does not execute, and you do not draw the card.
Clarification on Interaction
- The Reaction Window: You can react to the lab's ability while it is on the chain (RiftJudge FAQ #9570).
- Cost Payment: The cost for the Dusk Rose Lab (killing a unit) is paid during the resolution of that ability, not when it is added to the chain.
- If you want the draw: You must let the Dusk Rose Lab ability resolve. When it resolves, you choose whether to kill your unit to pay the cost. If you choose to do so, you then draw the card. If you play Hidden Blade to kill the unit before the lab's ability resolves, you have removed the fuel needed for the lab's ability.
This is my interpretation based on the mechanics of cost payment during resolution and standard chain interaction. No official FAQ exists for this specific interaction of killing your own unit to "pre-empt" the lab's cost.