Lyle would be open to meeting with Thancred and Rhy. He'll be sympathetic to their plight in his usual straightforward way. Unfortunately, he doesn't have any more information to give. He explains Castle Thorne communicates with Nott infrequently.

He'd agree to send the city guards, especially since he has a prior relationship with Thancred.

If there's any specific dialogue or interactions you'd like with Lyle, we can offer you a thread, Otherwise, you can presume the meeting was friendly, and that Lyle hasn't forgotten Thancred or Rhy assisting in Nott. He'll ask if they need any other resources. Nott is stretched thin, but he wants to help.