When an iPhone app is updated and the minimum required iOS increases, what happens for customers who still have the lower iOS?

When the user tries to install the update, the app store will alert the user saying something like "you must have iOS5 to install this update.". The user will still be able to use the current version they they have, though.

Nothing. The app doesn't create any problem until it is deleted. To be re-installed, it requires update, after being deleted once.

As a user, I've found that iTunes downloads the latest app regardless of what iOS the user is using on their device.

iTunes downloads the latest app and deletes (or asks to delete) older app versions from the user's iTunes library – an unwary user will click Yes to deleting the older version, and will be happy to get the latest version.

It is only when the user tries to install this latest version on their device (after removing the older app from their device) that iTunes will then raise the alarm that it is not compatible with their device.

The user is then left without the older version or the update.

It is Apple's hope that the user has backed up their iTunes library prior to downloading updates to their apps. This is a different procedure than just using iTunes to back up their devices, which only backs up the Data on the users' devices and not their apps purchased (downloaded) through iTunes.

If the user doesn't have a backup, Apple does not maintain older versions of apps. So the user has no means of retrieving older versions from the App Store.