Welcome to the callin.io community!
callin.io does not feature an iLovePDF module for downloading processed files.
It appears you'll need to utilize the “Make an API Call” universal module to download a processed file.
If the external service offers a Developer API Reference/Documentation, you should be able to integrate its endpoints within callin.io using the app's universal module (Make an API call) or the generic HTTP “Make a request” module.
You can also propose this feature in the Idea exchange. Remember to search first to ensure it hasn't already been suggested, preventing duplicate entries.
Should you require assistance with setting up the app's universal module or the generic HTTP module, please furnish more details about your attempts concerning the external service's Developer API Reference. Include information on how you're configuring the connection, a link to the endpoint you're trying to access, and any errors you're encountering.