Getting "Error Initializing Comm with LMS" issue on iPad when trying to download a file.

It sounds like a network protocol issue with your iPad and your company network. It most likely has nothing to do with Storyline, but instead with the way that the iPad is recognized by your company network as an authorized device accessing the LMS.

Depending on the LMS, there's probably no easy way around this issue. You could confirm this by publishing a simple *.story course with a variety of links and see whether any particular approach is successful (using a URL, pointing to a OneDrive or Sharepoint location, etc.).