Install old version of app on older iOS that can't be upgraded for whatever reason
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Try to install the app normally. It probably says it's not compatible with this version of iOS.

Download iTunes for business, version 12.something:
https://support.apple.com/en-gb/HT208079

Connect device to iTunes.

Set up syncing of apps.

Find app in the iTunes app store and download it.

Try syncing the app to the device. It probably fails, saying the device needs a newer version of iOS.

Go to the App Store on the device.

Try to install the app normally again. It should say it's not compatible, but this time offer to download an older version of the app.

Done!