  We construct infinitely many families of Lorenz knots that are satellites but
not cables, giving counterexamples to a conjecture attributed to Morton. We
amend the conjecture to state that Lorenz knots that are satellite have
companion a Lorenz knot, and pattern equivalent to a Lorenz knot. We show this
amended conjecture holds very broadly: it is true for all Lorenz knots obtained
by high Dehn filling on a parent link, and other examples.
