@Anonymous Apology for the delay and thanks for sharing the flow. APIM does have the Send request policy where you can call any specidied URL.
You can create the Request/Response connector that will generate the HTTP POST URL and you can use this URL in your send request policy of APIM with the request body that you need to send to the logic app. In logic app your workflow will have HTTP trigger along with the different data lake action (as per your requirement) that will communicate with the Azure Data lake.
Alternative you also use log to event hub policy for saving request or response context information for online or offline analysis.