It's simple in fact but this bug had me going crazy, very annoying indeed. All you have to do is the following:

1 - Select the Lantern in the inventory (Away from Darian or you will get the prompt to look at his inventory).
2 - Hold the Lantern Away from Darien, same way you would to give you more light.
3 - Keep the lantern on Hold Away from Darien and then go Near Him, Press the inventory button Near Him and you should be able to give Darien the medicine now, you migh need to do it twice.

Disclaimer - Works on every single one of these encounters, tested it myself.