Lease is used with these nouns as the object:
apartment, building, car, facility, land, premises, property, site

long, long-term
short, short-term
ten-year, etc.
commercial
operating (esp. AmE)
land
mining

have, hold
They have a lease with five years to run.

acquire (esp. BrE), buy, enter into, get, negotiate, obtain, sign, take, take on, take out, take up
She has taken out a new ten-year lease on the building.

grant (sb), sell (sb)
A freeholder may grant a lease of any duration.

renew
forfeit, surrender (both BrE)
They moved out and the lease was surrendered.

break, terminate
take over
transfer (esp. BrE)

run
The lease runs from April 19.

take effect (esp. BrE)
come up for renewal, expire, run out

agreement
payment

in a/the lease
a new clause in the lease

on a lease
The company holds the building on a long lease.

under a/the lease
Under the new lease, the rent would go up.

lease of
He took a lease of the premises. (esp. BrE)

lease on
The club has a 20-year lease on the property.

a clause in a lease, a condition of a lease, the provisions of a lease (esp. BrE), the terms of the lease
the length, period, term, etc. of a lease