Luna Replay supports the use of UnityEngine.Random in your games.
Problems may arrise if you are making use of asynchronous loading, as frames can occur out of order.
To workaround this you can make use of our Replay API's Barriers & Checkpoints functions.
In order to help debug Randoms Luna provides a debug option in the Capture and Replay UI in Unity. See more details about this here.
You can read more about setting up randoms with Luna Replay here.