Nutshell...

I used to be on the networks at two of my customers. One uses OCS internally. The other uses Lync.

I am contracting for them and want to be able to use Lync to communicate with both from home.

Can I do that? If so, what do I need on my side? (I am running Windows 7, and Office 2007.)

Will I be able to automatically save conversations?

Thanks.

If you're contracting for them, I'd have them set up an account for you that you can log into with a Lync client from home.  You can install Lync Basic for free.  Short of that, you'll want some sort of Lync server on your premises or use Office 365 and attempt to communicate federated. 

If you're using Outlook/Exchange on your end you could save conversations automatically otherwise you may need to cut and paste.