"In the top right corner, you have four icons :
full screen mode
close the window
Click on the first icon on the left. It will show the shared screen in full screen mode.
Below those four icons, you have a "Fit to screen" icon if all the presented content doesn't fit in your Lync window."
This does not display the content being presented in Lync full screen. It displays the content as only a portion of the Lync window, where a user may still even have to use scroll bars to view the content, along with several other brackets (e.g. chat box, participant list) around the content.
The short answer is that Microsoft Lync does not have the capability to view content in full screen.