Generally, a lease is a fixed-term tenancy and cannot be ended just by giving notice, unless that is stated in the lease. Otherwise, the landlord would be entitled to the same right and could give you a 30-day notice to terminate. The whole point of a lease is for both parties to have certainty of the occupancy period.It does happen that tenants break a lease, which is a breach of contract. In such a case, the tenant is obligated to pay rent through the end of their lease, but only until the property is re-rented. The landlord could also require you to reimburse their costs to re-rent the property. For example, the cost of advertising, a leasing agentu2019s fee, or prepping/cleaning the premises.If the tenant fails to pay for the vacancy and the security deposit is not sufficient to cover the landlordu2019s losses (rent and costs), the landlord is entitled to sue to recover.The landlord cannot double-dip by continuing to charge you rent after a new tenant has started paying.Check your local laws. Your area might have a tenant-landlord agency which can prinformation and help mediate disputes.