execute a command on amazon lightsail using aws-sdk-php

is there any thing in aws-sdk-php for that

No. The Lightsail API deals in modifying the resources in your AWS account. Lightsail doesn't have any control over the content of your instances after initial creation.

What triggers the PHP script?

• If you want the job to run at regular intervals you could install a cron job on the instance to trigger the script.
• If you want to trigger this on-demand from another service you can keep using SSH or create an HTTP endpoint to trigger it (using firewall rules or some sort of authentication to prevent public access; the advantage of HTTP is that you don't need to distribute the instance SSH keys).