There's a client-side Lync SDK, which is pretty easy to use if you're already a .NET developer.
It's easier to do something like this and have it running on every member of your small dev team's machine alongside Lync - easier than trying to re-invent a central conversation store.
I recently blogged about recording the length and status of Conversations, and also about identifying different sorts of Call within the Conversation (you'd be looking for Instant Message Call type).
After that, you'd need to subscribe to the Flow and catch every message to and fro, and log them to a database or whatever. There's a really good book which could help you with this: Unified Communications with Microsoft Lync. If you're serious about doing Lync development, this is definitely the book for you!