The recovery lap is part of the race. Walking it doesn’t mean you lost.

Recovery is part of the event rather than an interruption of it. The slow lap, the easy week, the deliberately quiet stretch are what make the next hard effort possible, and skipping them does not make you tougher, it only shortens the run. Moving slowly is still taking part. No rule says the whole thing has to be done at speed.

Schedule your easy stretch before your body schedules it for you. Walk the lap without apologizing to anyone for it. You are still in the race the entire time.