A true lydian has no leading tone, or tritone. It sounds more ZEN like. Rearranging the lydian structure, makes it something other than lydian. Lydian dominant means, and only means, that you take the lydian scale and b (flat) it's seven. The #4 (or b5th) becomes more tonal in terms of the b7th. More blues or American oriented. This idea really doesn't appear in any other popular cultures.