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I understand the problem is you have different passwords for Exchange Online and Lync Online.
Based on the current situation, I suggest you reset your password at Office 365 portal, so that you can use a new password in Office 365 services. You can request the administrator at your company to do so.
To reset a user’s password as an administrator, please refer to Reset a user's password.
If you have any additional questions, please feel free to post them in the fourm.
To reset your own password, you can use this URL, portal.microsoftonline.com/changepassword.aspx
Hope this helps,
How are things going on your side? Did my above information help you or do you need any further assistance?
I havent tried yet, as I can't do it by my self, as I am admin, and may not reset my own pw.
I'll be back. :-)