(2) After such apportionment the lessee shall, as to all future accruing rent, be liable to pay only so much of the rent as shall be so apportioned in respect of the residue of the land, and as to the residue of the land, and as against the lessee, the lessor shall have all the same rights and remedies for the recovery of such portion of the rent as previously to such apportionment he or she had for the recovery of the whole rent reserved by such lease, and all the covenants, conditions, and agreements of such lease, except as to the amount of rent to be paid, shall remain in force with regard to the residue of the land in the same manner as they would have done in case the residue of the land only had been included in the lease.