Acetyl L-Carnitine works wonders for cognition. I have fibromyalgia/chronic fatigue syndrome/ME and 4g with water in the morning wakes up my life! Amazing. From having a foggy brain, lethargic, tired all the time to bursting at the seams :)
I believe L-carnitine works if you have a deficiency.
L-carnitine is an amino acid that comes primarily from meat. So if you avoid meat you could have a deficiency. However, in that case the solution is simple: add some meat to your diet. The supplement is too expensive to be worth it.
The other possible reason is genetics. In that case I really don't know, because I don't know whether the genetic problem prevents you from absorbing L-carnitine or from utilizing it.
I have used it a couple times in the past, taking 1-2 grams prior to working out for roughly 3 consecutive weeks. It theoretically assists in the mobilization of fatty acids out of the cells to be used for energy. My personal thoughts are that it can make a slight difference when going from a low to very low body fat percentage (like say from 8 to 6% for males), but one will not notice a darn thing if they're in the double digits. It's really a fine-tuning thing. It also won't do much if you don't exercise and eat properly. So, if you really have everything dialed in and you just need to drop the last couple of body fat percentages, then it's an okay supplement to add in, IMHO.
(If you're a girl, aforementioned body fat percentages will differ)
Also, Dr. Terry Wahls recommends it for mitochondrial health. Like I said though, I've only used it for a total of 6 weeks, so don't know about long-term use.
l-carnitine is one of the few supplements i take. i take 1.5 grams in a liquid form (i get the swansons brand) with caffeine ( a cup of coffee) before i go to the gym. i've been using it for several years. i feel like it improves my stamina...which could help with weight loss in your case. i've tried the capsules of acetyl l-carnitine but prefer the liquid variety. good luck.
From my limited researching on l-carnitine & fatburning.
I didn't find anything in pubmed.
This page was pretty useful http://www.vanderbilt.edu/AnS/psychology/health_psychology/l-carni.htm
Even the T-Nation boys think its garbage. Majority of that board will injest anything for a 1% advantage http://tnation.t-nation.com/free_online_forum/diet_performance_nutrition_supplements/lcarnitine_3
Seems like Poliquin offers a positive take on L-Carnitine. But most of us will agree that any Poliquin dosage advice should be divided by 12. http://www.charlespoliquin.com/ArticlesMultimedia/Articles/Article/767/Top_12_Reasons_to_Use_Carnitine.aspx
I agree with everyone who said that the research shows it does not work. It has been extensively studied and has shown very little efficacy. Any possible benefits would be in particular populations, like athletes working on performance, but it's unlikely to help with fat loss.
Fat Loss Question 6 Answers
Muscle Gain vs Paleo 6 Answers