My left eye won't close all the way after double eyelid surgery? (Photo)

I wouldn't say this is "normal" or the intended consequence, but I do think that with time and some massage, your eyelid will loosen up and close down. It is of utmost importance right now, however, that you protect your cornea. I would sleep with your eye taped shut or with a generous amount of ointment.  

This is a fairly common complication of the surgery if too much skin was removed. It usually improves over time as the eyelid stretches but you need to see an ophthalmologist or oculoplastic specialist to make sure your eye is not getting too dry. This can be very dangerous and lead to permanent harm to the eye. I would definitely be putting an ophthalmic lubricating ointment in before bedtime and use preservative free artificial tears during the day.