A piano wire lasso has a problem with being very light for its rigid strength and surface area, and not going where it's wanted to go due to very little resistance to unwanted forces. Here's
a story about a guy using them to trap fish, but he has the loop deployed in the river beforehand as a snare, not a thrown weapon.
ISTR an earnestly fictional story where a guy uses some nasty sharp wire tied to two rocks. He grasps one rock in two hands and uses it to whirl the other overhead. He closes with the prey animal and the gives the wire a hard yank back and the far rock spindles around the animal's neck, fatally. This might work better with another guy to flush the animals past the rock guy, perhaps along a cliff face or defile.
Some grooved weights as for fishing might work to give the wire sufficient inertia to be thrown like a conventional lasso, but they'd need to be lightly clamped to avoid restricting the cinching of the noose, and might need to be replaced frequently as they fall of and are lost.