The app pool is not affected by LobbyCentral, and is a container that encapsulates the application from others. It is Windows method of keeping apps from crashing each other.
A 503 error means the app pool has gone offline. If you check it you will see that its state went from "Running" to "Stop."
The app pool is shutting itself down, most likely because Rapid Fail Protection is enabled. If it receives a certain number of exceptions within a specific time interval, it shuts itself off. The default is 5 failures within 5 mins.
Either disable Rapid Protection or set Maximum Failures, for example, to 2500. This will keep the pool from shutting off and making LC unavailable.
These settings will not cause any performance issues.
To get to the Rapid Fail settings, select the LobbyCentral app pool and then Advanced Settings.