How does the interaction between a Sprite token, Dusk Rose Lab, and Janna, Savior work during my Beginning Phase? Can I play Janna, Savior in response to the Dusk Rose Lab trigger, kill the Sprite token, draw a card, and then play Janna onto the battlefield in time to gain the Hold point?

Yes, this works — the Sprite gets killed, you draw 1, Janna enters the battlefield, and she'll be there for the Hold check.

Here's the exact sequence during your Beginning Phase:

1. Beginning Step (Rule 315.2.a): Both Dusk Rose Lab and the Sprite token's Temporary trigger fire simultaneously and become Pending Items on the Chain.

2. Finalize (FEPR Step 1): The Dusk Rose Lab ability finalizes — you choose to activate it, pay the cost by killing the Sprite token (this happens during finalization, before anyone can react), and "draw 1" becomes a finalized Chain item. The Temporary trigger also finalizes as "kill the Sprite."

3. Execute (FEPR Step 2): You now have Priority in the Closed State. You play Janna, Savior (she has Reaction, so this is legal timing). She enters the battlefield immediately upon finalization. Her "When you play me" trigger goes on the Chain.

4. Resolve: The triggers resolve in LIFO order — Janna's trigger heals your units and moves an enemy, then "draw 1" resolves, then the Temporary trigger fizzles (Sprite already dead).

5. The Chain empties → Beginning Step ends → Scoring Step begins (Rule 315.2.b), where you Hold all Battlefields you Control.

Janna (3 Might) will be on the battlefield when the Hold check happens, contributing to your control of that location. Keep in mind the Sprite is killed as the cost of Dusk Rose Lab's finalization — you don't need to wait for resolution, and you draw the card before Janna enters.