I had a lateral canthal suspension of both eyes for Lagopthalmos that didn't help. Will a canthoplasty fix it?

It is possible to get insurance to cover this since it is of medical necessity in nature. It sounds as though you have got weakness and paralysis of the upper and lower eyelid closure mechanism. A canthoplasty can certainly be performed and the lower lid brought up so that the cornea does not dry out. An oculoplastic surgeon with many years of experience who has performed thousands of these types of procedures would be the best person to look for.

In addition to treatment of the upper eyelid, it may be wise to resuspend the lower eyelid via a cheeklift, especially if a canthopexy has failed in the past.
With facial paralysis, the orbicularis (eye closing) muscle is deactivated. The cheek droops, literally like a weight dragging down the lower eyelid. Canthopexy or canthoplasty (especially if the lower eyelid is lax) is helpful but we have achieved our best results combining them with a cheek resuspension such as the USIC (ultrashort incision cheeklift).
This is also a good time to critically analyze the asymmetries of the eye, determine which are correctable, and address them.
Your problem is very technical and my colleagues have raised many excellent points and possible methods of repair.
Whatever the repair, no surgery reestablishes the nerve supply to the orbicularis muscle, so perfection, while a nice goal, is not realistic.

Dear A McMillen
This is a not so uncommon situation. I was able to help a woman with severe facial paralysis following the resection of an acoustic neuroma from the brain stem. She had numerous canthoplasties without success. I was able to make a significant difference for her with a surgery that I have developed to address these types of problems.
The key is to understand that simply tightening the lower eyelid, no matter how artfully, will never correct the situation. Generally the weight of the cheek must be taken off of the lower eyelid. This is done with an internal midface lift which is sewn to a hand carved ePTFE implant placed at the orbital rim. This material is placed to create an ultra-strong place to sew to. Next the lower eyelid has to be lengthened using hard palate graft borrowed from the roof of the mouth. Then a canthoplasty is used to adjust the tension and shape of the eyelid.