Does lymphedema tend to act up during pollen season?

Interesting question: I don't believe so, but i can't categorically tell you that we know the answer. Theoretically, it could make some difference, especially if you have severe allergies that affect the skin of your lymphedematous limb. That would be an unlikely situation. Be that as it may, I have never heard or read that pollen makes a difference.

Lymph: Lymphedema occurs when there is a compromise of the lymphatic circulation. This third circulation (arteries, veins) carries things too thick to be safely carried in arteries and veins like bacteria eaten by white cells and digested food. It is propelled along by normal body movements but contains a thick material called lymph. Blockage causes it to back up causing soft tissues/skin deformity.

Not really related: Lymphedema occurs when there is a compromise of the lymphatic circulation. Lymph circulation carries proteins and bacteria that are in tissues and outside of the blood circulation. Pollen & other environmental particles go to the sinus and lungs but do not enter the rest of the body so they don't get into lymphatic circulation.