Lambda function URLs are intended to be very lightweight way if invoking Lambda functions. They have limited capabilities, mutual TLS is not one of them.
If you need mutual TLS you should use API Gateway instead.
can we attach the custom domain to lambda function urls ?Accepted Answerasked 5 months ago
Supporting mutual TLS on specific resource pathsasked 7 months ago
Is there a way to recover the deleted lambda function?asked 2 months ago
CloudHSMv2 Force "TLS client-server mutual authentication" or disable default key on HSMasked 9 months ago
Client VPN connection issues - TLS Handshake issueasked 4 years ago
Is Lambda Function URLs fixed?asked 3 months ago
Mutual TLS for AWS Lambda Function URLasked 5 months ago
Mutual TLS with Commercial Client Certificatesasked 6 months ago
AWS API Gateway private integration with mutual TLSasked 10 months ago
AWS WAF with AWS Lambda Function URLs?Accepted Answerasked 2 months ago