Just use the same logic as the session class itself.
if ((time() - Session::activity()) > (Config::get('session.lifetime') * 60)){ // Session expired}
Place this in your 'before' filter - and it will run on every request.
Why not do this?
if (!Session::has('name')){ $sessionTimeout = 1;}
If a session times out then the name will no longer be set. You can then write some code to respond to $sessionTimeout == 1;
BTW,Specifically if you need the session lifetime,
Use this:
{{ session('lifetime') }}
When describing this,
session(['User' => $user, 'lifetime' => 3600]);