It can be used either way. The dictionary may say that the owner leases, but in everyday conversation we say "I am leasing this car" and "she leased that building"

Technically, to lease means you own the property and are allowing someone else to use it. However, it is sometimes used to mean 'to rent from someone else' for a set period of time. Confusing, I know. We also hear people colloquially saying "I'm going to rent (out) my apartment" - meaning allow someone to use it. Same issue of a term being used in two different ways.