In windows, on all browsers, I'm able to click on either of the following two a tags and the lync client will open and function as desired.

<a href="sip:sip@address.com">test</a>

<a href="IM:<sip:sip@address.com><sip:sip2@address.com>">test</a>

On a mac it tries to open parallels or it opens IChat.  In windows I'm asked if I want lync to be the program that opens and if I click yes it works as expected.  I have to think there is a means by which to set this up on a mac or mobile device as well as long as the lync client is installed. 

Does anyone know how to do this?

I verified that the sip <a> tag will open the lync client on an IPHONE, but I can't for the life of me figure out why it doesn't work on Safari or Firefox on a MAC.  I feel like it should just be a matter of telling the browser how to handle a link. 

Agreed. I would recommend that you consult the Firefox or Safari support engineer.

I haven't figured out how to do this yet but am curious about the same thing. I found documentation on how to change the old Messenger Application to register the SIP URI to it so I had/have hopes that I can do the same with Lync.

Here are those instructions for reference:

Messenger for Mac. The click-to-chat feature, in which a user can click a link to begin chatting with another community member, will only work if the SIP: protocol is associated with the chat client. In the Macintosh case, Messenger for Mac does not automatically register itself as the default application for links using the SIP protocol (on Windows, Microsoft Office Communicator does).

In order to best support users on Messenger for Mac, consider modifying the Messenger application's plist file, then distributing the modified Messenger application to users. Note that both Chrome and Firefox will prompt the user to approve launching the Messenger application on their first use of click-to-chat. By choosing the launch the application and "remember the choice," they should be able to avoid future prompts.

To modify the plist file:

1. On a Macintosh computer, in the Applications folder, right-click the Microsoft Messenger application, then click Show Package Contents.
2. In the Contents folder, open the Info.plist file.
3. In the editor where the file opens (on a Mac, this will likely be the Property List Editor), add a new array for the CFBundleURLTypes key.
   • If the key doesn't yet exist in the property list file, add it with the values shown below (this is an XML view of the property list file -- it will appear different in the Property List Editor).

     <key>CFBundleURLTypes</key>
         <array>
             <dict>
                 <key>CFBundleURLName</key>
                 <string>SIP Address URI</string>
                 <key>CFBundleURLSchemes</key>
                 <array>
                     <string>sip</string>
                 </array>
             </dict>
         </array>

   • If the key does exist, add only the new <dict> stanza shown.
4. Save the plist file, close the package contents, and distribute the modified application to Macintosh users.