on lease 根据契约；以租赁的方式。
on the lease 在租约上。这里lease noun [ C ]租约，租契。
=a legal agreement in which you pay money in order to use a building, piece of land, vehicle, etc. for a period

【例句】
He has the house on a long lease.
他长期租用该公寓。

These machines are available only on lease.
这些机器只供租用。