Can you react to Dusk Rose Lab's ability during the Beginning Phase, even if there are no units at the battlefield?

Ruling: No. Dusk Rose Lab's ability does not automatically go on the chain. The ability reads "you may kill a unit you control here to draw 1," which means you choose whether to use it at the start of your Beginning Phase. If you choose to use it, killing a unit is a cost paid during finalization. If you have no units at that battlefield, you cannot pay the cost, so the ability cannot be finalized and is removed from the chain before opponents can react.

Sequence:

• At the start of your Beginning Phase, you decide whether to use Dusk Rose Lab's ability (it is optional due to "you may").
• If you choose to use it, the ability becomes a pending chain item.
• During finalization, you must kill a unit you control at that battlefield as a cost.
• If you cannot pay the cost (no units present), the ability is removed from the chain.
• If you pay the cost, "draw 1" becomes the finalized chain item, and the chain becomes closed, allowing reactions.

Nuances:

• The unit is killed as a cost during finalization, before opponents receive priority to react.
• "You" and "your" in battlefield abilities refer only to the battlefield's Controller per Rule 187.6.c.