I have already bought a dictionary via in-app purchase but I am being asked to pay again to reinstall it or to install it on my other devices.

Once you have paid for a dictionary, you should not be required to pay again to re-download it to your device or to install it on another of your iOS devices.

Firstly, please ensure that you are signed in to the App Store with the same Apple ID you used to make the purchase. Then, in the Catalogue tab of the app, tap Restore. This should allow you to access in-app purchases made with this Apple ID, i.e. to download your dictionary again at no further cost.

For more information on restoring in-app purchases, please see this Apple support page.