i have lync 2010 on premise and office 365, users mailboxes are on 365

how can i use lync 2010 on premise for my office 365 unified messaging

Hi,

please use the links in the matrix here; http://technet.microsoft.com/en-us/library/jj945633.aspx in order to offer you initial guidance.

Regards
Ben

Here's a nice checklist for you: http://help.outlook.com/en-us/exchangelabshelp/gg702674

You'll need Lync 2010 enabled for enterprise voice, so it can accept calls from your telephone provider, it will also need to have the edge role deployed with a third party certificate.  From there, you connect Lync 2010 to UM using the above guide, traffic will pass through the edge over the Internet up to Office365.

For configure Lync with Office 365 UM, you can refer below link

http://www.lynclog.com/2012/02/lync-2010-on-prem-cloud-um-integration.html