Thank for reaching out. We’re gonna try to update the API wiki to include that in the next couple of days.
What i would recommend you to do (and its what i do all the time when i have to script something against the API) is to open your browser’s developer tools to check the network transactions, and then open Octopus from the web and try to A) open a lifecycle and modify it or B) Create a new one and then check the sent and received info to see how the JSON is supposed to look when you do the POST.