Can a mammogram show whether a lump is benign?

Not definitively: Due to the limited sensitivity/specificity, in majority cases, mammogram can only give you a suggestion/impression that it possibly is malignant or a benign. It can not tell you a definite answer. To increase sensitivity/specificity ultrasound needs to be done. However, if you have a palpable lump, a tissue biopsy should be the test to do- to differentiate whether it is benign or cancerous.

No: Only a biopsy will tell for sure if a lump is benign.

Sometimes: Some masses have specific characteristics on mammo that enable the radiologist to make the diagnosis of a benign lesion, without biopsy. These include: hamartoma, oil cyst, calcified fibroadenoma, fat necrosis, lymph node, calcified cyst. For most other lumps, further imaging, follow up, or biopsy are likely needed.