In  R.F. Williams showed that all knots in the Lorenz template are prime. His proof included the cases where any number of positive twists were added to one of the template’s branches. However  does give an example of a composite knot in a template with a single negative twist. Below we will show that in all the negative cases composite knots do exist, and give a mechanism for producing many examples. This problem was cited in a list of problems in dynamics in [1, problem 4.2].
Sullivan, Michael C. "Prime Decomposition of Knots in Lorenz-like Templates." (Jan 1993).