I've been ramping up and down with L-Carnitine Fumarate ( I have the Acetyl, but have never tried it) since last November. I have almost always taken it on an empty stomach and I can feel it go into me about fifteen minutes later. I'm not sure the effect would be so marked if I took it with food and have read here, I think, that it is less used by the digestive process when taken without food. Though I could be making that up!
What is absolutely true is that I need it and it is helping me to heal--I have begun to feel my muscles again, I stretch all the time--a sensation that I hadn't even noticed was missing until it made a surprising comeback, and I have those well, embarrassing feelings of sexual arousal that I haven't had since I was a teenager. Not constantly, of course! I think this has something to do with stimulation of progesterone...
From this article on Female infertility:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5785901/
there was this quote: "They have shown that treatment with ALC [Acetyl L-Carnitine] increases serum levels of other reproductive hormones, like estradiol, progesterone,..."
Anyway, oddly, when I don't have enough one of my symptoms is chills, so it certainly has an effect on the HPG axis. And this particular scholarly article indicates that it can have a profound effect on fertility.