Hi William,
According to your description, may I know if you have installed Lync client on your Mac in following articles?
http://community.office365.com/en-us/blogs/office_365_technical_blog/archive/2011/11/16/mac-users-download-lync-for-mac-2011-today.aspx
http://www.microsoft.com/en-us/download/details.aspx?id=36517
If the client has been installed correctly, could you following the steps below to troubleshot this issue and let us know the result?
Make sure that you have followed the correct steps when you sign in to Lync Online
1. Start Lync for Mac.
2. Enter your email address, user ID, and password.
3. Next to Sign in as, select the presence status that you want to display after you sign in.
4. If you want to save your credentials, click to select the Remember my password check box. Your credentials will be saved in the Mac OS Keychain and will work until the next time that your password changes or expires.
5. To configure additional options for connecting to Lync Online, click Advanced. You can configure the following options:
o Manual Configuration: Select this option if automatic configuration is failing, and specify the following values:
Internal server name: sipdir.online.lync.com:443
External server name: sipdir.online.lync.com:443
o Kerberos authentication: Leave this option cleared. Office 365 uses the Windows Azure AD authentication system for authentication.
In addition, could you try to sign in to Lync Online by using an incorrect sign-in address. That is, a sign-in address that you know won't work. For example, \EmailAddress @contoso.com and let us know if the error message is the same.
Regarding to SkyDrive, I would like to explain that the SkyDrive and SkyDrive Pro are different. Office 365 P1 plan is using the SkyDrive Pro.
Different between SkyDrive and Sky Drive Pro: http://sharepoint.microsoft.com/blog/Pages/BlogPost.aspx?pID=1033
The SkyDrive Pro is not available for Mac currently.
If you have installed the SkyDrive client or App (Not SkyDrive Pro), it will occur this error message.
Here is a thread for your reference: http://community.office365.com/en-us/forums/153/t/127652.aspx
Thanks,
Wilfred Ying