[Obligatory disclaimer: I am not a lacemaker, but my very geeky SO is (and a knitter and weaver and so on and so forth) and often delivers discourses on the subject and several of my friends have been similarly inclined math geeks who knit & such.]

To a first approximation a lot of them are - simple geometric/topological rules applied in a loop, a small number of branches, occasionally recursion. There's a huge amount of technique and no small amount of technical knowledge in making them work with a relatively high friction material with variable tensile strength & stretch. Execution on this stuff often involves keeping more mental state than most of the programming I do so clearly it's not always as simple an automata as it might seem, but there's a kinship.