As of now, a unit affected by Flaming Lasso cannot be moved by spells at all (with the exception of few spells which only move straight upwards). This is kind of a sad interaction.

It would be much better if it the target could still be moved normally, but not beyond the break distance of the lasso, which is supposed to be 425.

This is one of the things Warcraft 3 dota did better than Dota 2. Not only does it look better, it also has more applications than how it works in Dota 2.

In the vid, you can see a comparison between WC3 dota and Dota 2. In the old dota, you can push lassoed units within its break range.