可以使用AWS Lambda函数来处理API Gateway的WebSocket连接，然后将元数据保存在连接会话中并传播到断开连接事件。

以下是一个示例Lambda函数，演示了如何附加元数据到连接会话中并在断开连接时使用元数据。

import json

def lambda_handler(event, context):
    # retrieve the connection ID from the event
    connection_id = event["requestContext"]["connectionId"]

    # retrieve any metadata from the event or any other source
    metadata = {"foo": "bar"}

    # append the metadata to the connection session
    endpoint = event["requestContext"]["domainName"] + "/" + event["requestContext"]["stage"]
    apigw_management_api = boto3.client("apigatewaymanagementapi", endpoint_url=endpoint)
    apigw_management_api.post_to_connection(ConnectionId=connection_id, Data=json.dumps({"metadata": metadata}).encode("utf-8"))

    # return success response
    return {"statusCode": 200, "body": "Metadata appended to connection session."}