As per the message received from INZ General Manager last night:
If you cannot provide information required by the online form, such as a new medical certificate, upload an explanation instead to complete your application.
So you can lodge an online application without a medical, but it's possible that INZ won't look at it until after lockdown. Then again, jobs in supermarkets may be regarded as essential workers so it may be that they will triage your application and process it with the staff they
apparently have working from home (some LIA's have been told different things, INZ haven't confirmed that this is the case).