Apple's policy is that if you acquire an app, free or not, the app should be available to download to any of your personal devices. However, as the app is updated, it's requirements may change and prevent fresh downloads on older devices. Example: If you attempt to download AMPLIFi Remote to an old device, and the minimum iOS version is 11 or above, you'll get an installation error:
"This application requires iOS version 11 or later. You must update to iOS 11 in order to use this application."
To get AMPLIFi Remote onto the older device, you'd have to first acquire the app via iTunes on a computer, or via the App Store on a device that is running the required iOS version, then download the app on the older device. Note that iPhone-only apps won't appear on an iPad, and vice versa. For our example, we'll use iTunes.
Use the search box for the name of your application.
Select the app in the search results.
Click the Buy or Get button to acquire the app (you don't have to download it).
Use your older iOS device and search for the exact app in the App Store or click on the Purchased icon in the lower navigation bar. When you locate the app, click the Install button.
After you click Install, you'll see a popup indicating that there is an older version of the app available for download. Click Download to install the last compatible version.