Sorry to hear you have lung cancer. How is your treatment going? So, have you ever heard of raynauds's disease? The tips of the fingers turn blue/purple with this based on temperature changes due to poor circulation. Here is information on it https://www.mayoclinic.org/diseases-conditions/raynauds-disease/symptoms-causes/syc-20363571
Read that and see if it sounds like what is going on. Definitely check in with your doctor about it.