Do Kubernetes liveness probes run in parallel with your application?
Liveness probing done by kubelet in each node. And yes, it runs in parallel with your application.
In you case, you could touch /tmp/healthy file each time you start new iteration in loop. And use command like find /tmp/health -mmin +0.5 in health check. This command returns nothing if file is older than half a minute. If health check command returns nothing it's assumed that check is passing.