Firewall rules for Mysql on Lightsail

Hi, @Dataedo.

Unfortunately the database in Lightsail cannot cover your needs.
Lightsail database don't have source filtering like security group.

You can create Amazon RDS as another option.
And if you want to connect to your RDS database from your Lightsail instance, you can use the VPC Peering feature to connect Lightsail's managed VPC to your default VPC.

Please refer to the following article. (Sorry, Japanese Article)
https://dev.classmethod.jp/articles/lightsail-vpc-peering/