Sure, establishing a new Virgin airline would allow a lower cost base
How? You pay the same for aircraft, fuel, landing fees, the pilots already pay for their endorsements in Virgin anyway, passengers pay for food already.... there are not many areas to actually save anything other than labour. You can save money by being small and simple but once you grow the business then you just run into all the same problems all over again.
Given that Jetstar is severely propped up by QF I would hardly call them a successful LCC. Ryanair, Southwest, Easyjet have managed to make it work independently and from scratch. Jetstar is the vehicle that QF management used to destroy the high labour costs in QF.....nothing else.