General:
* Reata: A long rope used for lassoing.
* Lariat: A rope with a loop at one end used for catching livestock.
* Rope: A general term, but can be used to describe a lasso.
* Catcher: A more abstract term, referring to the action of lassoing.
More specific:
* Bola: A type of lasso with multiple weights, often used in South America.
* Bozal: A kind of lasso used to catch animals by the head.
* Hackamore: A lasso-like device used for training horses.
Figurative:
* Entrap: To capture or restrain.
* Bind: To tie or fasten.
* Snare: To trap with a rope.
The best word to use will depend on the specific situation and the tone of your writing.