Despite my best attempts, my hireling died. Alas poor meatshield, I knew her well. It does not seem that her equipment dropped when she died. Is it lost forever? If I hire a new hireling will the new one inherit her equipment?
Your hireling still has his equipment. You can resurrect your hireling for a fee at any of the NPCs where you would be able to hire a new one, or at Tyrael if you happen to be in Act 4. After resurrection, the hireling will have all the same equipment it had at time of death.
If you hire a new hireling, however, all that equipment will be lost forever.