Does Dusk Rose Lab trigger before scoring? And does it go on the chain without paying the cost aka removing a unit? Can you put on chain then decline?

Yes, Dusk Rose Lab triggers before scoring. The Beginning Phase has a Beginning Step (where "at the start of Beginning Phase" effects happen) followed by a Scoring Step where Hold occurs (Rule 315.2). The card's own text even notes this: "(This happens before scoring.)"

No, it does not go on the chain without paying the cost. Because the ability says "you may," you choose at trigger time whether to place it on the chain at all (Rule 383.3.a). If you choose yes, it becomes a pending item. During finalization, you reach the Pay Costs step — you must kill a unit there as a cost. If you cannot pay (no unit), the pending item is removed (FAQ #10373).

You do not put it on the chain and then strategically decline. The "you may" decision happens first — if you don't intend to kill a unit, you simply don't put the ability on the chain. There is a secondary safety net under Rule 404.2 (you can decline to pay during Step 4, removing the pending item), but this exists for cases where the cost becomes impossible between trigger and finalization, not as a free "change my mind" after committing. If you want to use the Lab, you choose to put it on the chain intending to pay; if you don't, you leave it off entirely.