Hello Henry,
One caveat I want to make in terms of my last response was that all of my experience has been with Lync 2013, and the articles I provided were for Lync 2013. Therefore, the advice may or may not apply to Lync 2010. Given your symptoms, however, it sounds
like the exact same behavior. Also, the fact that users with one email account setup in Outlook are not having the issue, and ones with multiple accounts are having the issue, would indicate that there is a pattern there to pay attention to. If the behavior
is the same between versions, then I would say those articles answer the question. They would need to have the default account be one that matches the login address for your Lync client.
Eric has suggested that this mismatch issue would not be a problem for this. While I am all ears on his response, I would be interested to see the Microsoft documentation to back that claim, as my experience in our environments has always been the opposite,
and the Microsoft documentation that I provided above indicates that the mismatch issue is in fact a problem for Conversation History (unless I read it wrong, or that article strictly apples to 2013, and NOT 2010). One way to find out would be to test the
recommended client configuration in those articles for users that have multiple email accounts, and see if it fixes your issue.