No. The lease does not end before the date set by the court. The landlord must initiate legal proceedings. The court will check, for instance, whether the correct notice period has been observed and whether the statutory ground for termination cited does justify the termination. If this is the case, the court will set an end date and an eviction date.
An exception applies if the tenant himself terminates the lease or agrees to the termination by the landlord. In that case, the lease does terminate on the notified end date and the tenant must have vacated the building by that date.