I think about your scenario,

Solution one :
Let both of them to add item  
in their baskets and at the end of their sessions
that decide to confirm their shopping, if item catch by some one give  Correct Sign to another.

Solution two :
Don't let both of them to add  item to their baskets and keep your item
Sync, that it means  you should risk about some item in some times Lock or disable to choose  about it And attention to this advice that you should keep item Sync because until item quit (Give Up) from some one, item shows UnLock.

But if you could keep Sync your Object in all sessions of customers, it (Solution two) is better, because your customers don't wanna waste their time  and return to choose another or find out it is like a joke to choose their favorite Item.