Lambs lettuce does not like dry conditions, so that did cause the mildew. It sounds bad enough that you need to cut or clear the worst of the damage,, a long job.
In future you could either sow a week or two later, or keep it watered. I sowed late (Pusar on Sep 6th) and its small but healthy. I was sent a pic from the Lake District of some huge and healthy lambs lettuce, helped I imagine by the extra moisture up there.
The show was good thanks, lots of keen gardeners, people loved the huge and beautiful sugarloaf chicory and Filderkraut cabbage.