Lambda function with AWS managed layer

When you say your Lambda functions are an "image" I'm assuming you mean that they are container images.

Unfortunately, you can't use Lambda Layers with container images - a container is defined to be self-contained; adding libraries/code to it during the launch phase isn't available. You either need to package the libraries and code needed into the container during the build process; or use a Lambda function that isn't launched from a container image.