As I said, one needs to through Lenovo's service parts channel, not their sales channel.
What I always do is call the service provider (in Israel it's IBM), and they have a department which can sell replacement parts by FRU. I imagine something similar exists in all countries.
Out of curiosity I just called them today and inquired.
You have to give them the FRU for the part, not the marketing number. FRUs are available in the HMM (Hardware Maintenance Manual).
For the Z61t, for example, these are the numbers:
92P1121/92P1123 - 4-cell
92P1125 - 7-cell
Usually, the original FRUs are no longer manufactured, but there are replacement FRUs. The service department will have in their system to find the updated numbers.
For the Z61t this is what they came up with:
42T4614 - 4-cell
42T4616 - 7-cell
Now, you can buy it directly from them (I was quoted 3 business days for delivery).
You can also buy these original batteries, new, from third parties, for example Thinkpad-Parts:
http://www.thinkpad-parts.com/42T4614-Thinkpad.html (currently $127)
http://www.thinkpad-parts.com/42T4616-Thinkpad.html (currently $97)
The prices are usually high, and not always consistent. For instance, the price IBM Israel quoted me for the 4-cell was lower, but for the 7-cell it was higher. Looks like on Thinkpad-Parts you can make offers and negotiate the price somewhat. Never tried this, don't know if it's effective.
There is always the eBay channel. It is possible to get genuine batteries on eBay, sometimes even new. But it's difficult, because some of them do sell fakes that pose as genuine. I don't know if it makes any practical difference or not. But if you really want a genuine part, it may require some effort to prune the fakes from the reals if you are going down the eBay route.