I am very sorry your grandson has lymphoma.
It is not unusual for chemotherapy treatments for lymphoma (or any cancer) to have to be delayed due to low white blood cell, red blood cell, and/or platelet counts. Chemotherapy medicines kill rapidly dividing cells in the body, including tumor cells, normal young cells in the bone marrow, and the cells that line the GI tract. If chemo is given when the blood counts are too low, the risk of infection or severe bleeding is extremely high. All protocols (treatment plans) have specific guidelines as to what the normal blood counts must be to give the next round (doses) of medicines.
This lowering of normal blood counts does not mean the treatment either is or is not working for the lymphoma. The fact that your grandson's eyelid is more fully open is a good sign. His doctors will probably do another scan (likely an MRI or CT scan) after his first 10 weeks of chemo to see how much the tumor has shrunk.
I hope this helps to answer some of your questions, and please tell me if you have additional questions.
I do wish your grandson the best.
Louise Sivak, M.D.