Is there a trap anywhere in that scheme for the tub? Lead is pretty inert, so if it doesn't get flexed, or you didn't try to run a snake down it, it could last for eons. I assume that if you did need to gain access, you'd have to tear up the ceilings below?
Is there any evidence of water spotting or rot near the shower or the toilet? If you find that, then you've probably isolated the leak. Both the shower and toilet are more likely to be the culprits than the drain itself. For tiling info, highly suggest you check out www.johnbridge.com.