You have to specify lambda layers as ARNs in terraform using layers parameter:

layers - (Optional) List of Lambda Layer Version ARNs (maximum of 5) to attach to your Lambda Function.

Using the following syntax in terraform:

layers = ["layer-arn"]

For example, the ARN for AWSLambda-Python27-SciPy1x in us-east-1 region is:

arn:aws:lambda:us-east-1:668099181075:layer:AWSLambda-Python27-SciPy1x:24

If you not sure what is your ARN, you can create a dummy a Python 2.7 lambda function, add AWS layer AWSLambda-Python27-SciPy1x layer, and the console will give you its ARN.

After determining that the declared resourced is in a declared module, and that the resource's exported attributes are absent from the module's declared outputs, we can solve this by declaring the exported attribute as an output for the declared module. This is because exported resource attributes exist only within the same config namespace, and must be accessed using the namespace nomenclature.

Inside the config for the lambda-layer module source, you need to add a declared output:

output "mm_layer_arn" {
  description = "arn for the mm lambda layer"
  value       = aws_lambda_layer_version.mm_layer.arn
}

You can similarly output the entire object of exported resource attributes by assigning aws_lambda_layer_version.mm_layer to the value, but this is mostly useful if you need to access or otherwise iterate on that object.

This output will now be accessible from the namespace of the config where the module (in this situation lambda-layer) is declared. Since module name is declared in the same config as the lambda-layer declaration, that module declaration can now access the output in the appropriate namespace:

module "name" {
  ...
  layer_arns = [module.lambda-layer.mm_layer_arn]
  ...
}

You can read more about module output namespace in the documentation.