lease liability

sir my text states that lease liability meets the definition of a “liability” as per Conceptual Framework. Now, liability as per Conceptual Framework is “Present obligation to transfer an economic resource as a result of a past event.” But what am struggling to understand is how the lessee has a “PRESENT” obligation to transfer cash as a result of coming into the lease contract? I mean its understandable to say the there is a Present obligation for the current lease liability portion, but not so for the non-current portion of the lease liability, if you get what am trying to say…