amazon web services – Replay Cloudwatch logs are sent to a lambda

I subscribed to a lambda for many Cloudwatch protocol groups to process, index, and analyze these logs.

Everything works fine, but I want to play a large amount of old logs with this lambda.
I try it by retrieving logs about the aws logs get-log-events CLI, but I can not find an easy way to do this because the data is structured.

First, the lambda is called with a coded / gzip blob in a Json {"awslogs": {"data": "H4sIAAAAAAA .... I can do it easily, but it's expected that the blob itself is structured like this:

{
    "messageType": "DATA_MESSAGE",
    "owner": "...",
    "logGroup": "/aws/lambda/...",
    "logStream": "2019/08/02/($LATEST)...",
    "subscriptionFilters": (
        "..."
    ),
    "logEvents": (
        {
            "id": "34402224585553617062605662326569493632889831387406598144",
            "timestamp": 1564703999832,
            "message": "..."
        },
        ...

And the issue of aws logs get-log-events is nowhere near this structure.
I could try to rebuild it myself, but it gets boring. And some fields are missing (eg logEvents.id)

Do I miss another easier way to render logs on my Lambda?