Eclipse had no reason to believe that Animus, a fellow thearch and upstanding mage with a history of service, would lie to him. But still, he could understand where some needed to be convinced of certain things.
Lyle delivers two invitations. One to Tyria's office that in somewhat subtle language apologizes for any confusion and requests her presence at his home for confirmation of Animus' claim, in a "private setting, far from unworthy eyes."
The invitation he sends to Animus is worded as a request, but he gets the impression that its not optional.
In either case Lyle waits around until such a time as either party gives him a response.