How can I use Lua script in the "Script" field of a specific conversation line in **Dialogue System for Unity** to call a method from my C# script

when you have a problem with a third-party vender product, the best plan is always to contact the provider directly. An asset author will list their contact info on their store page.

The author of Dialogue System for Unity is active on the asset’s own thread
https://discussions.unity.com/t/released-dialogue-system-for-unity-easy-conversations-quests-and-more

and also Discord. See the asset listing on the asset store for the discord link.