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If your lashes turn inwards and rub on your eye, then the condition is called entropion. Your insurance would pay for surgery because of this.
If your lashes don't turn inwards and you just have excess skin weighing down your lids, then the condition is called dermatochalasis. Whether you insurance pays for this depends on how much effect it has on your vision (upper visual fields). You have to have a visual field test done (with eyelids taped up and untaped). You have to have photos of your eyelids and the extent of the drooping. Your doctor will also have to have some statement of medical necessity. Then, depending on all of that, the insurance will evaluate whether or not the drooping is bad enough for you to need surgery.
If you have to pay out of pocket, I would count on $8000-10,000 in hospital and $5000-8000 in ASC.
Hope this helps and thank you.