Actually it is not possible to run the Lync client on Linux. The "lync Web app" client does not work on Linux even with the binaries of the mono project. For the time being Microsoft doesn't say if they have it on their road map.
There are third party Linux clients (including one that Microsoft qualified, the snom embedded client that does presence and enterprise voice). The protocol documentation makes it possible for the Linux community to build such clients. There is no Microsoft built full client, but the Microsoft OWA web client is supported on Linux and delivers IM and Presence.
You can try The SIPE Project, which is a third-party Pidgin plugin for Microsoft LCS/OCS.
The SIPE project develops a third-party plugin for the Pidgin
multi-protocol instant messenger. It implements the extended version
of SIP/SIMPLE used by various products such as Microsoft Office
Communications Server, Reuters Messaging, Microsoft Live
Communications Server. With this plugin you should be able to replace
your Microsoft Office Communicator client with Pidgin.
It is not recommended to compile the source code yourself. Experience
has shown that it is difficult to get all prerequisites correctly in
place, especially for new Linux users. Instead you should use the
ready-to-use installation packages which most OS distributions offer
under the name pidgin-sipe.
The snom enterprise solution utilizes the comprehensive unified
communications functionality of our Unified Communications partners'
solutions to provide large scale enterprises and corporations with a
complete communications system: snom devices are compatible with both
of these partner’s unified communications solutions whilst remaining
as fully functional and interoperable devices in their own right.
This means that not only can you take full advantage of all the rich
presence, video conferencing and communications management strengths
of unified communications, but you can also sleep easy in the
knowledge that if you decide to switch to a different enterprise level
solution in the future, you will not need to ditch the phones.
Also, it seems like Pidgin, is being mentioned a lot with regards to Lync.
Pidgin is a chat program which lets you log in to accounts on multiple
chat networks simultaneously. This means that you can be chatting with
friends on MSN, talking to a friend on Google Talk, and sitting in a
Yahoo chat room all at the same time.
Pidgin runs on Windows, Linux, and other UNIX operating systems.
Sources, and more information:
Microsoft Lync Qualified Products
Microsoft Lync on Linux