No, the Lync Client SDK isn't for websites. There are Silverlight controls available, but they will only work if the user has the Lync Client installed, which is probably not true for your website.
For text only chat, you could look at UCWA, but you'd have to handle file-sending yourself. There's currently nothing that can do voice in a browser, but UCJA/jLync was announced at the Lync Conference 2014 Keynote and should be able to do that.
I actually blogged about the different APIs available and what they are all for yesterday: http://blog.thoughtstuff.co.uk/2014/07/lync-development-picking-the-right-api/