Lipid droplets are indeed droplets of fat, but they're actually proper organelles in their own right, with a protein coat and a complex system of regulation that varies depending on cell type: Brown fat, for instance, has on its lipid droplets the Perilipin-5 protein, which supports basal or constant breakdown of fat, in order to keep you warm. Meanwhile, white fat is dominated by perilipin-1 and needs to be induced to give up its stores of fat. A holy grail in weight loss would convert white into brown fat --- as long as you're careful not to overheat to death.
This work started in the summer before my senior year of high school. Desperate for something to do, I sent an email to the Science Dean at my local university (LTU, where I eventually went for my Master's). I asked her, Dr. Hsiao-ping Moore, whether I could do research under her, and was invited in to talk--- after I clarified that I was not looking to get paid, of course. My mom drove me to that interview. Supposedly, the reason Dr. Moore agreed to the internship was that I said "I didn't understand anything in her papers, but that I wanted to". And so, I was able to get a year of mentorship in practical wet biochemistry prior to starting my degree in it.
My final independent project involved growing cardiac muscle cells (annoying, though watching them beat is pretty cool) to test for common lipid droplet proteins, and try to transfect (introduce) gene expression for missing proteins. Below is a poster presentation I gave on the topic, and then a review on the perilipin family of proteins that I wrote a couple of years later at university.