I have a sole temporary "Glasc Mixologist" in Dusk Rose Lab, at the beginning of my turn can I trigger the Dusk Rose Lab battlefield on my temporary mixologist, and can I play the brought back unit onto Dusk Rose Lab?

Yes, you can perform both actions.

According to RiftJudge FAQ #9428, because both the Temporary keyword trigger (which would kill your temporary unit) and the Dusk Rose Lab ability trigger at the start of your Beginning Phase, you as the controller choose the order in which they resolve.

Sequence of Events

1. Beginning Phase Starts: Both the Temporary trigger and the Dusk Rose Lab ability are added to the chain.
2. Chain Resolution: You choose to resolve the Dusk Rose Lab ability first.
3. Cost Payment: You kill your temporary Glasc Mixologist as the cost for the Lab's ability.
4. Effect: You draw 1 card.
5. Deathknell Trigger: Because Glasc Mixologist died, its Deathknell ability triggers and is added to the chain as a pending item (Rule 734.1.d.2).
6. Chain Resolution: You resolve the Deathknell effect. You may play a unit from your trash to the battlefield where Glasc Mixologist died (the Dusk Rose Lab).
7. Temporary Trigger: Finally, the Temporary trigger attempts to resolve. Since the temporary unit is no longer on the board (it was already killed to pay for the Lab), the instruction to kill it cannot be followed and is ignored.

As confirmed by RiftJudge FAQ #9329, you are permitted to play the unit from your trash to the battlefield where the Deathknell unit died, even if that battlefield becomes unoccupied when the unit dies.