Can a former landlord charge me two months additional rent as a lease break fee if they rented the place immediately?

Typically a landlord can only charge you for the amount of time that the house is vacant, and then only if you broke the lease in such a way as the landlord could not reasonably re rent the premises. Otherwise a residential landlord cannot charge additional rent from you when he is receiving rent from another new tenant. The reason is that, since the landlord cannot rent the same space to two tenant and collect two rents, he cannot recover damages from you which would represent as second rent. It is not often brought, but there is a legal claim to made by the landlord if the landlord had to re rent the premises at a lower rate than you would have paid over the life of the lease.