The root of the problem is that a scheduled process on the instance is exhausting the cpu burst capacity of the instance.
Understanding how cpu capacity works in Lightsail should help resolve the issue: https://lightsail.aws.amazon.com/ls/docs/en_us/articles/amazon-lightsail-viewing-instance-burst-capacity#baseline-cpu-performance
There is a tool named "cpulimit" that can be used to limit the CPU utilization of running processes or launch new processes with such limits. It is not installed by default on Lightsail's WordPress blueprints but can be installed by issuing the command
sudo apt install cpulimit. The idea is that you would modify the cron jobs so that they cannot take 100% of the CPU and consume your instances CPU credits.
I hope this helps!
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