The special Lightsail VPC

Normally when you use Lightsail, you can't connect to other AWS resources from your Lightsail servers (e.g: you won't be able to connect to an RDS database). This is because your Lightsail resources are inside their own special VPC, and thus they can't see your RDS database, which is in another VPC.

Your AWS account has a default VPC for a given region. Most resources you use that reside within a VPC use this default unless you specify another. Lightsail resources use a separate VPC of their own which you do not control.

You can, however, use VPC Peering to allow Lightsail instances to connect to resources in your default VPC. Go to the Lightsail Console, and in the Settings -> Advanced area, you can enable VPC peering for a given AWS region. Note that if you don't have any Lightsail instances in a region, that region won't appear in the VPC peering options until you make one. The setting is per-region, so you don't have to change it for each Lightsail server you create.