Lightsail has a VPC peering feature.
However, you can only peer with the default VPC.
If you have an RDS resource other than the default VPC, you can place the NLB in front of the RDS and use the endpoint service to establish a connection route from the default VPC to the RDS with an IP address target.
I have successfully connected to Lightsail-> Endpoint on Default VPC-> NLB-> RDS with this configuration.
Lightsail Windows Server 2019asked 6 months ago
How Instances in Private subnet can connect to Internet with NAT InstanceAccepted Answerasked 2 months ago
How can Ec2 Instance in private subnet access internet via vpc endpoint?Accepted Answerasked 3 months ago
Lost access to Windows serverasked 2 years ago
Can't connect to MySQL db from Lightsail instance. MY-010055 warning in logs.asked 9 months ago
Placing a Bastion in a Private Isolated Subnetasked 8 months ago
Unable to connect to EC2 instance in private Subnetasked a year ago
Unable to connect to EC2 instance in private Subnetasked 2 years ago
Connect Lightsail instance to AWS instance in a private subnetasked 5 months ago
EC2 instance in private subnet shows IPv4 address of NAT instanceasked 3 years ago