My lower eyelid is red and puffy but there is no pain or itching?

Many causes. A red and puffy lid could be infected, inflamed, irritated, allergic, blepharitis, etc. If not improving, should be evaluated in the office.
Tear duct inflammed. Tear glands sometimes get inflammed, which will cause swelling and redness. Cool/wa compresses help. At times, it is necessary to see your doctor.
Possibly. This may be blepharitis or inflammation of the lids sometimes related to a low grade infection and sometimes related to blocked glands in the lid. You can try some warm compresses and gentle massage of the lid. Gently washing the lids with baby shampoo may also help. If this persists then i would recommend seeing your eye doctor.