If this saves you an hour, I have done my due diligence.
In short, if you’re trying to get a new Win7 machine going with Office 365, installing the Lync client is the first step.
Except the download won’t "start."
I even ran Process Monitor against it to see what it was doing, and the install is in an endless loop looking for an MSI registry key that doesn’t exist.
Well, there IS a workaround, but I had to dig for it.
Look for a nice post from a helpful Microsoftie here. This helped me out, and hope it will help you out too.