Is it safe to apply lotion on a 2 month baby's face?

Yes But....... Lotion is okay sparingly and only very mild lotions. I often recommend cetaphil or aquafor some creams and lotions can create rashes. Most rashes on the face are caused by their own slobber and contact with linens, blankets and clothing. The rashes wax and wane. Wipe the face often with a wash cloth and this will help too.