Presuming you run a Rohloff box, the chain is supposed to be slack. The Chainglider in effect holds the chain on the gearwheels if it gets slacker. In ten years or so, I've had the chain drop off inside the Chainglider only once, and that was because a runaway bungie got its hook tangled in it.
With a Chainglider, unless you've dragged it through water, or ridden it on very wet roads for hours (in which case you want to get longer mudflaps!), you don't open it merely for inspections. You will not believe until you've seen it how tightly it encloses the chain.
As for lubing, I operate KMC X8-93 chains (the lowest order of protection in the X8 series)
on the chain lube for the entire life of the chain, which I expect to be about 4500+km because I'm heavy on chains (previously, with daily lubing, inside Dutch chain cases, I got about a 1600-2000km out of a chain). Matt, also on this forum, got 10,300 out of the more expensive KMC X1 (now renamed by KMC).
My previous lubing regime, until 2011, is described here:
http://thorncyclesforum.co.uk/index.php?topic=3561.msg15494#msg15494 Note that at that point we still didn't know that the Chainglider is a very durable piece of gear.
At
http://thorncyclesforum.co.uk/index.php?topic=2233.0 you can see a) where we started on the Chainglider journey, and why it is the only chain case I recommend, or that is discussed here.
The original factory lube inside a Chainglider experiment is here:
http://thorncyclesforum.co.uk/index.php?topic=6813.0 and the thread also contains lots of discussion of the Chainglider
Good luck!