In that case I say we grab everything, we are kind of at war with Westeros, and the Tyrells haven't sent us any indication, that they will be on our side when we invade.
My problem was more with taking it after they got it, in case they decided to support us during the reclamation, would be awkward for them to support us, only for us to turn around, and take one of the Reachs greatest treasures from them, taking it before they ever get it however, that I can get behind.
My concern was more that I thought Lothos would negotiate with them himself, and if he agreed to let them have the crown, then it would be awkward to take it away from them later.