Here's how to get the Blue Dragon summon disc:

1. In Cloudius, once you've beaten Baruk, search his chair before you leave to find an Egg.

2. Once the Aethersphere covers the whole world, take the egg to Lilith in Linea. She will beg for Stahn to give it to her. Being the kind-hearted soul you are, Stahn will give it to her.

3. After a certain amount of time has passed, when you enter Stahn's house an event will occur in which a baby blue dragon will hatch from the egg.

4. Feed the baby dragon all 4 Goumets (A-D) and it will become an adult dragon and give you the Blue Dragon Disc!