Cannot connect to MySQL on lightsail from lambda

I have a MySQL server on a lightsail instance. The goal is to access the MySQL server from a lambda function.

What I did is as follows.

• Turn on VPC peering of lightsail
• Create a MySQL user with '%' host
• Add the following policies to the lambda function (AmazonEC2FullAccess, AWSLambdaBasicExecutionRole, AWSLambdaVPCAccessExecutionRole)
• Open port 3306 on the firewall of the lightsail
• Comment out the bind-address in /opt/bitnami/mysql/my.cnf and reboot MySQL

The lambda code and app.py for CDK are below. The result is the following error. If I try to connect to the same MySQL server with the same code from another EC2 instance in the same VPC/subnet, I can connect successfully.

What do I miss?

[ERROR] OperationalError: (2003, "Can't connect to MySQL server on 'host' (timed out)")
Traceback (most recent call last):
  File "/var/task/hello.py", line 13, in main
    con=MySQLdb.connect(host=host,db=db,user=user,passwd=pw,charset="utf8");
  File "/opt/python/pymysql/connections.py", line 353, in __init__
    self.connect()
  File "/opt/python/pymysql/connections.py", line 664, in connect
    raise exc

Lambda function (hello.py)

import pymysql as MySQLdb;
    
def main(event, context):
  print("hello");
  con=MySQLdb.connect(host=host,db=db,user=user,passwd=pw,charset="utf8");
  print("done");

app.py

from aws_cdk import (
    aws_lambda as lam,
    aws_iam as iam,
    aws_ec2 as ec2,
    core,
)
import os;

class MyStack(core.Stack):
    def __init__(self, app: core.App, id: str) -> None:
        super().__init__(app, id)


        vpc = ec2.Vpc.from_vpc_attributes(
            self,"VPC",
            vpc_id=vpcid,
            availability_zones=[zone],
            isolated_subnet_ids=[subnet],
        );
        sg = ec2.SecurityGroup.from_security_group_id(
            self,"SG",
            security_group_id=sgid,
            mutable=False
        );

        layer = lam.LayerVersion(
            self, "MyLayer",
            code=lam.AssetCode.from_asset('./lib'),
        );

        lamrole = iam.Role.from_role_arn(
            self, "LambdaRole",
            rolearn,
        );

        helloFn = lam.Function(
            self, "hello",
            function_name='hello',
            code=lam.AssetCode.from_asset('./code'),
            handler="hello.main",
            timeout=core.Duration.seconds(900),
            role=lamrole,
            vpc=vpc, # for mysql
            security_groups=[sg],
            layers=[layer],
            runtime=lam.Runtime.PYTHON_3_7,
        )

app = core.App()
MyStack(app, "hello")
app.synth()