I ask, since you get into the realm of using two databases simultaneously, which is more complicated. OK, so we've established that you want to use sqlite - great.
On the basis that you're using 1.1, have you looked at the plugins to see what session storage modules you could use?
This snippet is a bit old, but may still help:
http://snippets.symfony-project.org/snippet/7
Give all the above a go, and let us know how far you've got.