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A Lorenz link is equivalent to a T-link, which is a positive braid built byconcatenating torus braids of increasing size. When each torus braid except thelargest is obtained by full twists, then the T-link can be described as theDehn filling of a parent link. In this paper, we completely classify when suchparent links are hyperbolic. This gives a classification of the geometry ofT-links obtained by full twists when the amount of twisting is large, althoughthe bound on the number of required twists is not effective. We also presenteffective results on hyperbolicity for two families of T-links obtained bytwisting, even when the number of twists is small. Finally, we identifyfamilies of satellite T-links obtained by half-twists.

Hyperbolic and satellite Lorenz links obtained by twisting