Can you activate the Battlefield Dusk Rose Lab multiple times in one turn before beginning phase?

No, you cannot activate the ability of Dusk Rose Lab multiple times in one turn, nor can you activate it outside of the Beginning Phase.

According to the card text, Dusk Rose Lab has a triggered ability: "At the start of your Beginning Phase, you may kill a unit you control here to draw 1."

Here is why you cannot activate it multiple times or outside of that phase:

1. Specific Timing: The ability is a triggered ability that specifically triggers "At the start of your Beginning Phase." It is not an activated ability (which would be denoted by a cost followed by a colon, e.g., [Cost]: [Effect]), so it cannot be activated manually during your Main Phase or at any other time.
2. Triggered Once: Triggered abilities occur automatically when their condition is met. In this case, the condition is the start of your Beginning Phase. Once that phase begins, the ability triggers once.
3. Scoring/Turn Limits: Even if you had a way to trigger the ability multiple times (which this card does not provide), you are generally limited by the rules of the game regarding how many times you can score or interact with a battlefield in a single turn. As confirmed by RiftJudge FAQ #6122 and #7023, you cannot score a battlefield multiple times per turn, and game actions are generally restricted to prevent infinite loops or unintended multiple activations of triggered abilities.

In summary, the ability is restricted to a single, automatic trigger at the start of your Beginning Phase.