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 Android devices. However, you must ensure that you are using the same Google Account that you used to buy the dictionary originally.

For more information on restoring purchases, please see this Google Play support page.

For more information on switching between Google Accounts, please see this Google Play support page.