Do my locked days survive a plan update?

Yes — that is exactly what locking is for.

As your plan advances, a locked day keeps the workout (or the rest day) it was holding. TrainAsONE plans around your locked days rather than changing them.

Locking only freezes the days you have chosen. TrainAsONE keeps analysing your runs and continues to update the rest of your plan, so locking a few days does not stop your training from adapting.

Note: one deliberate exception is a training pause. Setting or changing a pause deletes locks (and per-day rules) dated before the day you start training again — those days are rest days, so a lock there could never be honoured. See How do I pause my training plan?.