How long can you delay the breast lump removal a doctor advised?

Why wait?: If it is cancer you need to get started, if it isn't you can stop worrying. Waiting is the worst option and a form of denial. Schedule it and get it over.

Need biosy results: With rare exception, one should not go to the or without a tissue diagnosis. This is usually easily accomplished via needle biopsy under local anesthesia. Once the diagnosis is established, the timing of the surgery can be guided by whether the lump is benign or malignant: if benign, no urgency; if malignant, why wait?

Don't wait: Is there a particular reason for waiting? Insurance coverage maybe? Otherwise, as others have posted, it seems like a definitive diagnosis of your lump is needed. If it is malignant, you need to get treatment, and if it is benign, you can rest easy. Is this lump amenable to needle biopsy? That would be the preferred option over surgical excision in most cases.