Forfeit generally denies relinquishment or loss, and yet it is the term used to describe the landlord's role in the dance as they resume possession of a place. What is behind this?
Forfeit can be used as a verb. When the landlord "takes steps to forfeit a lease" it means that the landlord is causing the lease to be canceled, to be placed in forfeiture. It is the tenant who forfeits right in such a case, but the landlord who takes action. to say "the landlord forfeits the lease" is short for "the landlord places the lease into forfeiture". Yes this usage can be confusing, but it is quite common.
Merriam-webster gives as sense 2 of entry 2 for "Forfeit":
to subject to confiscation as a forfeit
That is the sense being used here.