Low cost will survive because it will be the last option between going or staying home. $200 saved on a $700 fare is smaller % wise than $200 saved on a $500 fare but it is still $200. work out the "earnings" to be had in flying low cost vs full service, $$$ saved divided by number of hours flown, it can be considerable.
During a down turn people will down grade from first to business, business to economy and economy to low cost.
During an upturn people upgrade in the opposite direction and people who wouldn't normally have flown go low cost.
If prices go higher expect some of the lower end business travel to be low cost as well. The accountants will be under pressure to find savings and downgrading company travel is an easy one.
An LCC is under no pressure to have a network and can simply drop underperforming routes and start new ones in the blink of an eye. If they have X number of airframes they simply put them where the money is.
Not all low cost airlines will survive but I bet Ryan Air will.