Please don't forget to lock the door.

Literal

Not-forget-[without-ず] door [at-に] key [object-を] apply-[polite-request-てください]

ドアに鍵 vs ドアの鍵 captures a small grammatical contrast worth noticing. Here the door is the target of the locking action (に), not the owner of a key (の). Both express the same real-world action but via different framings — the の version treats 'the door's lock' as a unit, the に version treats the door as the target of the verb.