To accomplish this task, you will need to setup a "Public" OneDrive folder (Anyone with link can view).
Then, host your desired .ZIP file in the "Public" folder.
In OneDrive online, create a link to the .ZIP with permissions: Anyone with link can view.
Now, in an Incognito Window, navigate to your URL for the .ZIP.
Open "Inspect Element", then monitor the network traffic while you click on "Download" on the page.
You now have a direct link to your OneDrive file!
In order to download it into LabVIEW, open an HTTP handle, make a first GET request to OneDrive's recommended sharing link, then a second GET request to the direct URL you found earlier. The body of the second GET request is your file in binary form.
To convert it into a ZIP, use "Write Binary File", wire the body string directly into the write (after having opened/created a binary file), and viola, you now have downloaded a ZIP from a public OneDrive link in LabVIEW!