Once you begin to cast the spell, losing control of Raul won’t affect the spell.

If you cast a spell from among cards in your graveyard that were milled this turn using the permission granted by Raul’s first ability and then have a new Raul, Trouble Shooter come under your control in the same turn, you may cast another spell from among cards in your graveyard that were milled this turn.

You must follow the normal timing permissions and restrictions of the spell you cast from your graveyard.

If you are instructed to put a card into your graveyard from your library without using the word “mill,” (by the effect of Rowan’s Grim Search from Wilds of Eldraine, for example), Raul’s first ability won’t allow you to cast it.

If you cast a spell from among cards in your graveyard that were milled this turn using another permission, Raul’s effect doesn’t apply. You can cast another spell among cards in your graveyard that were milled this turn using the permission granted by Raul’s first ability.

You must pay the costs to cast that spell. If it has an alternative cost, you may cast it for that cost instead.