Can I have eyelid surgery, but keep my monolid? (Photo)

Even though you have monolid on both eyes, left eye may have very small fold just above the eyelashes. To match,  you can create same size of fold on the right side. I don't call this double eyelid rather to match the eyes same. This can be done as non cutting method.

Eyelid asymmetry is not uncommon. It can be due to brow position, more eyelid skin on one side, structure of the bones around the eyeball or even problems with the primary muscle that elevates the upper eyelid. Corrective surgery can be done while preserving your monolids. A thorough examination is necessary to come up with the right treatment plan. Good luck!

Absolutely yes!  The key to this surgery is making the incision low down near the lashes and removing just the right amount of skin to match the left.  It is very straight forward but I would recommend consulting with an oculoplastic specialist with experience in Asian eyelid anatomy.  Good luck!