If the insurance policy lapses after a claim has been submitted for a minor accident will it affect the claim processing?

The claims department will be concerned only with the status of the policy at the moment of the accident. Other than that, it will not come into play. Any delay would be very minor (as long as it takes someone in the coverage dpt to determine that there was coverage on the date of loss). However, if the insurance was lapsed on the day of the accident, this will, of course, cause there to be no coverage for the accident.