Having just finished 9 months of chemo, a lap sized quilt she can take with her to treatment is a great idea. The treatment rooms are usually kept at a comfortable temp for the staff, but lying in a recliner with IV's running into you can chill anyone and the blankets they have just didn't cut it with me. I recommend a cotton pieced top and flannel backing with a warm batting in the middle. This will keep it fairly light to carry. Rag quilts can get extremely heavy to carry. I was tired and weak after each treatment and don't know if I could have managed a tote bag with a heavy quilt in it. Thankfully hubby accompanied me each week and carried my tote bag for me.
I second using either her favorite colors, or cheerful colors. There are lots of free patterns. Warm Wishes makes up quickly and you can use a beautiful focus fabric for the square. Using a quick pattern will let her be able to use it during and after treatment.
I wish your friend good luck. Caught early, breast cancer is very treatable and with the tests and technology now days, they can pinpoint the best treatment for a successful outcome. I had a stage 1 breast cancer 29 years ago before genetic testing and just finished treatment for stage 4 ovarian cancer. Yes, I am one of the lucky ones who have the BRAC-1 gene mutation and got both types. In remission now and celebrate each day that comes along.