DNS lookup for RDS times out

Question

I have an RDS instance my_instance and a lambda. Both sit on the same VPC.

The RDS has a SC my-security-group-rds and lambda another security group my-security-group-lambda.

my-security-group-lambda has outbound rule without constraints. All protocols with IP 0.0.0.0/0.

my-security-group-rds has an inbound rule that allows any access from my-security-group-lambda.

Inside the lambda I want to perform DNS resolution of the hostname:

def dns_lookup(domainname,record_type,*dnsserver):
    """
    Get dns lookup results
    :param domain:
    :return: list of dns lookup results
    """
    try:
        lookup_result_list = []
        myResolver = dns.resolver.Resolver()
        if not dnsserver:
            lookupAnswer = myResolver.query(domainname, record_type)
        else:
            myResolver.nameservers = dnsserver[0]
            lookupAnswer = myResolver.query(domainname,record_type)
        for answer in lookupAnswer:
            lookup_result_list.append(str(answer))
        return lookup_result_list
    except Exception as err:
        logger.exception("Not able to lookup DNS:{}".format(err))
        raise

I first perform the dns_lookup on the rds regional server, which works out nicely.

listOfAuthoritiveNames = dns_lookup("eu-west-1.rds.amazonaws.com", "NS")

Then I try to perform dns lookup on my instance:

dns_lookup("my-database.dfafda.eu-west-1.rds.amazonaws.com", "A", listOfAuthoritiveNames)

This gives a timeout. If I use a wrong hostname for the database it says that there is no record, so it would seem that it has access to the nameservers.

Any idea what might be missing?