Can lidocaine be used as an alternative to novacaine to alleviate pain from a broken tooth?

Absolutely : Lidocaine is a good choice that is commonly used in dentistry.

Yes, by a dentist: Lidocaine is a very effective and commonly used local anesthetic. When administered by a dentist it can be used to treat a variety of painful dental conditions including fractured (broken) teeth.

Same : Novacaine is a common layperson term for local anesthesia. Lidocaine and xylocaine (lidocaine) are the same drug and the most common used.

Lidocaine: Lidocaine rinse is a topical anesthetic. Depending in virulence of causative reason for pain, it can only provide some temporary relief as problem worsens. For example, infection deep inside a tooth spreading to surrounding bone and every organ with a blood supply will not be helped by a topical liquid. Toothache most often means infection. Fracture is 2nd most common cause.