Your point being that regular soap has no melting point?
The point being when your hot-process soap is at gel, it has melted. You can't make it any runnier except by adding water based liquids.
It's like chocolate -- when it melts, it's melted. You can make chocolate runnier or thinner only by adding fat, not by making it hotter.
"...Can you (or anyone else) provide a source for the claim that a lipid in the gel phase cannot be melted to the liquid phase through the application of heat?..."
Okay, let's back up. Lipids? Who is discussing lipids? You yourself posted your question in the lye-based SOAP forum, "... I'm curious if anyone has ever tried to turn up the heat at the tail end of hot process, just prior to the "pour?"..."
Edit: As I acknowledge in Post 21 below, I accept that pure soap is a type of lipid. But knowing pure soap is a lipid as well as triglycerides are lipids is no more useful in answering the OP's question than saying soap is a salt and table salt is also a salt, so therefore soap and table salt should behave similarly. One has to look deeper than these very general family associations for the answers. End edit.
I can only conclude you asking a question about SOAP made with a hot process method. So the question is NOT about lipids -- we're talking about soap. They're not remotely the same. What source can YOU provide to substantiate your perception that soap IS a lipid?
Fats from which soap is made -- triglycerides -- are lipids. Soap is the salt of a fatty acid. Soap and lipids are entirely different chemicals, and they have entirely different phase diagrams. At the temperatures and pressures that a hobby or small scale soap maker can create, soap becomes thinner or thicker only by modifying the water content.
"...I maintain that if you can't find a source, but continue to claim it as fact, then you are claiming to have made a new discovery. In that case, my recommendation to contact NASA is merely sound advice, and not an insult at all...."
No, YOU need to do you homework and get your chemistry facts straightened out. After you really know what you're talking about, I will be glad to discuss this matter further.