I think it is a known issue. I notice the lag when mine left with 2.39GB free space. The magic number seems to be 3GB or less. Tom's hardware did a test on this. Soft reboot does not resolve the problem.

http://www.tomshardware.com/news/Nexus-7-J...mark,17503.html

Then I deleted a few movies. Manage to recover more than 4GB. Speed is back to normal.