Update: This issue only effects MAC users who have Dial-in Conferencing configured on their Lync Online account. This issue has been replicated by MS support and they seem to have indicated that it is a 'bug' on their end. But we have not been told when to expect a fix.
Temporary Workaround: We just happened to stumble into a temporary solution. If the Admin removes the Dial-in Conference configuration (for example, we use PGi) for each MAC User and then re-adds the configuration, the Outlook 2011 Online Meeting button works again. NOTE: Wait a few hours between removing and re-adding the DIal-In configuration. It seems to take a while (I don't know the exact time) for changed settings to effect the operational features. In fact, what I did was remove the settings on a Friday and then add back on Sunday or Monday (we are a small company with only 10 people affected by this, so easy for us).
Downside: Since this issue happened in the first place and the root cause was not fixed, I'm guessing that the MAC User's Online Meeting button will stop working again within a month or 2 (about how long they worked to begin with).