That one is tricky, but there is an upcoming alerting feature in Dynatrace release 212 (rollout in the next 2 weeks) that helps to solve that.
This feature allows you to alert on missing data.
So my proposed way would be:
1.) Define a log metric that writes a 1 for all kind of log lines
2.) Define a custom event for alerting if the number drops below a threshold AND alert if metric shows missing data (meaning no log lines are written anymore).