I showed this journal to a friend who suggested a simpler framework. There are two changepoints we care about: the lactate threshold, at which point the lactate in the blood begins accumulating over some baseline value, and the aerobic threshold, at which point the lactate concentration begins to increase at an even faster rate. These changepoints will be evident in the data as a change in slope of lactate concentration with heart rate. This suggests a simple linear model with two changepoints.
Given this simpler framework, I can fit a simpler model: a piecewise linear model with two changepoints. This is a well-established model with well-maintained software to fit it, e.g., the python package piecewise-regression.