There is no law on lift repairs, per se, but there are laws about responsibility to repair and maintain common property as well as a landlord’s responsibility to provide basic services.
Basically you need to contact your landlord to tell them to put pressure on the Owners Corporation and/or strata manager to get this fixed as soon as possible.
You might also say that you need them to make an arrangement to help get your father out of the house, at least on occasion, or reduce his rent so you can afford to make the arrangements yourself.
Contact the Tenants Union on tenants.org.au for more advice.