在AWS Systems Manager Automation Document中使用Lambda别名时，自动化文档不会自动更新别名。如果要更新别名，需要在文档中设置一个步骤，并使用Lambda SDK来更新别名。

以下是一个使用Python SDK更新Lambda别名的示例代码：

import boto3

# Enter the region your lambda function is in.
region = 'us-west-2'

# Enter the AWS service client you will use to update the alias. Here we use 'lambda'.
client = boto3.client('lambda', region_name=region)

# Enter the name of the lambda function you want to update the alias for.
function_name = 'my-lambda-function'

# Enter the name of the alias you want to update.
alias_name = 'my-lambda-alias'

# Enter the ARN of the new version you want to point the alias to.
version_arn = 'arn:aws:lambda:us-west-2:123456789012:function:my-lambda-function:2'

# Update the alias.
response = client.update_alias(
    FunctionName=function_name,
    Name=alias_name,
    FunctionVersion=version_arn
)

print("Alias updated successfully!")

将这段代码添加到AWS Systems Manager Automation Document中并调用它，就可以自动更新Lambda别名了。