Dear Radical
There are a number of issues here:
Dry eye-any eyelid surgery can worsen an already dry eye. If the eyelid surgery is sufficiently aggressive, the eyes never recover from this. Presumably your potential surgeon took a detailed history, carefully examined your eyes including measuring your vision, studied your corneal surface to look for evidence of dryness, and measured the ability of your eyelid to produce tears, and discussed what to expect regarding eye comfort and dryness. If this has not been done, then your surgeon as not adequately examined you.
Epicanthoplasty. This is a procedure to change an inside fold to an outside fold. The epicanthus is the fold that extends from the inner corner of the upper eyelid. Taking an inside fold to an outside fold is generally not a good idea. One simple reason for this is that the scar has no place to hide. It can be done and it can look great or it can be horrible. Generally I do not recommend it. Some surgeons do it because they think that it is their job to erase any Asian vestiges from an eyelid. WIll you be happy with the result? I would advise an abundance of caution here.
Lateral canthoplasty. A good idea if you want to do surgery on someone but you really are not sure what surgery to perform. WIth any luck, you will have a non-result. Yes there are clinical circumstance where a canthoplasty is appropriate but in a healthy person simply looking to enhance their Asian eyelid, it is seldom indicated.
Is there a reason your surgeon is not performing double fold surgery for you? You live in Los Angeles. I recommend that you see some additional eyelid surgeons to reduce the likelihood that you are about to wreck your eyelids with a surgeon who does not know what they are doing. Something is troubling you or you would not have posted a question. Try looking up eyelid surgeons in Los Angeles on this site. Be certain that your potential surgeon is board certified in ophthalmology and a Fellow of the American Society for Ophthalmic Plastic and Reconstructive Surgery.