Sorry to hear that you singed your eyelids! Fortunately, you did not suffer a serious burn!
You should rest assured that your eyelashes are just like any other type of hair on your body. They hair follicles that produce the eyelashes are constantly working and producing new lashes, so your eyelashes should grow back without any trouble at all. The rate at which eyelashes grow back is highly variable, so it is hard to say exactly how long it will take for them to grow back in your case, but certainly within a few weeks you should have new eyelashes.
Unfortunately, there is not much you can do to speed up the rate at which the eyelashes grow back. What you can do is avoid anything that would put mechanical stress on the eyelashes and cause them to fall out, as this will make your eyelashes look even more sparse than they already are. In particularly, you might want to avoid eye liner, mascara, and other forms of eye makeup until your eyelashes have grown back in all the way.
If you have any other concerns about this issue, feel free to contact your primary care doctor
, who will be happy to answer your questions.