Você só precisa atribuir a quantidade de espaço para que as mudanças aconteçam. De uma receita nos documentos :
A snapshot volume can be as large or a small as you like but it must be large enough to hold all the changes that are likely to happen to the original volume during the lifetime of the snapshot.
No entanto, certifique-se de alocar espaço suficiente:
If the snapshot logical volume becomes full it will be dropped (become unusable) so it is vitally important to allocate enough space.