Hi there! In the context of leases, I would definitely go for "desalojo". In Argentina, that is the legal term we use to refer to "eviction".
I looked up the term "desahucio" at the RAE website and I discovered that it actually exists. I don't know if you use it in Spain or in some other country. Perhaps, you could tell us which is the terminology you use in other Spanish-speaking countries.
Please note that the term "evicción" does actually exist in Spanish, but it means something different. It's a contractual warranty a transferor grants when conveying property thereby warranting quiet enjoyment or good title to the property.
Hope it's useful!
