When a temporary unit with Deathknell is on Duskroselab, can you use Dusk Rose Lab before the temporary unit does and trigger both the Deathknell and the draw 2 effect?

To answer your question: Yes, you can use Dusk Rose Lab to kill a Temporary unit with Deathknell, which will trigger both the Deathknell effect and the Dusk Rose Lab effect (though note the Lab allows you to draw 1 card, not 2).

Because both the Temporary keyword (which would kill the unit) and the Dusk Rose Lab ability trigger at the start of your Beginning Phase, you control the order in which they are placed on the chain and resolved.

Sequence of Events

1. Beginning Phase Starts: Both the Temporary trigger and the Dusk Rose Lab ability trigger. As the controller of both, you choose to place the Dusk Rose Lab ability on the chain first.
2. Chain Resolution: You resolve the Dusk Rose Lab ability first.
3. Cost Payment: You kill your Temporary unit as the cost to use the Lab. This draws you 1 card.
4. Deathknell Trigger: Because your unit was killed, its Deathknell ability triggers and is added to the chain as a pending item.
5. Deathknell Resolution: You resolve the Deathknell effect.
6. Temporary Trigger: Finally, the Temporary trigger attempts to resolve. Since the unit was already killed to pay for the Lab, the instruction to kill it cannot be followed and is ignored.

As confirmed by RiftJudge FAQ #9428 and #9633, this sequence is valid, and because the Deathknell trigger is created while the unit is killed, you are able to resolve it fully.