The order you put the materials in doesn't really matter. When the air is turned on the material fluidizes, or should. That means everything moves, almost like a washing machine. When the air turns off the material falls back out of suspension and sorts itself into layers. That's why it doesn't matter what order the material goes in because the filter will layer the material itself.
It's kind of a whole deal getting the amount of air right. Has to be enough to cause the material to fluidizes or it doesn't clean very well, but not so strong that it blows sand out of the barrel.
Lava rock would require a lot of air to be moved. You might want to reconsider that.
There's a ton of info on these filters, they've been around awhile. Often called "sand & gravel filter". They are meant to be used to "polish" water meaning there are other filters before the S&G to remove larger stuff. That allows for cleaning less often so only need cleaning every week or two depending on the pond. They can be used by themselves but may need to be cleaned much more often.