I do not raise this particular orchid but this web site indicates that a rich cimbidium media is about right for this orchid.

http://www.speciesorchids.com/GRAMMATOPHYLLUMELEGANS.html

I have this variety however mine is not as large as yours. My experience with almost all my orchids are that they bloom more frequently when they are a little tight in the pot. This type although the leaves are more soft and pliable can grow in full sun. I have mine in a bark mix in full sun. I think lava rock would be fine as a growing medium as well. I think if you pot it up in too large of a pot, the plant tends to put a lot of it's energy into filling the pot with more root growth which can delay blooming. Hope this helps a little. Aloha