I used Lubuntu 16.04 via a plain Live USB and a Live USB with persistence. In both, I had a mouse attached via USB cable to my laptop and both the mouse and touchpad were functional. I didn't try unplugging the mouse.
To my mind, there is no difference between Lubuntu 14.04 and Lubuntu 16.04 in this regard.
Code:
06:56 AM ~ $ uname -a
Linux vasa1-Inspiron-1545 3.13.0-83-generic #127-Ubuntu SMP Fri Mar 11 00:25:37 UTC 2016 x86_64 x86_64 x86_64 GNU/Linux
06:56 AM ~ $