Latisse has no antibacterial in it, so to minimize the risk of contamination and infection, they encourage you to use different brushes for each eye. Revitalash, their competitor, has an antibacterial so the risk is less.
When the FDA approved Latisse they recommend that you use a disposable brush for each eyelid. The reason for this is to prevent infection and contaminated Latisse product. The product comes w/ 60 applicators for this reason. If you were to use the same applicator for both eyes, you must not touch the sterile Latisse bottle to the used applicator. Dr. Grant Stevens