Tumor cells do use more glucose, because their mitochondria doesn't use the glucose as efficiently, energy wise, as mitochondria in non-cancerous cells. (1 molecule of glucose normally = 36 molecules ATP, the major energy carrying molecule, but in tumor mitochondria another pathway is active that only makes 2 ATP per glucose and the waste products are what are thought to lead to tumor proliferation, and increased acidity.)
I'm not sure if you can really take from that that you should avoid glucose to prevent the tumor from eating, although there are plenty of other reasons to avoid processed sugar. Lots of complex molecules are broken down into glucose that the tumor cells and other normal cells can use.
DLBCL is diffuse large B-cell lymphoma, and mine is pretty aggressive. If anyone has any specifics regarding supplements that have worked for them I'd appreciate hearing them. I also have a couple of scientific journal articles I can share on natural anti-cancer compounds.
Everything I have read in medical journals so far points to supplements either helping or not affecting the efficacy of chemotherapy drugs. The problem is, most of the studies are in petri dishes or animals, so the interactions in humans are still unknown and probably will be for a long time, since the natural compounds aren't patentable and the drug companies have no incentive to help fund the research. And human trials are very, very expensive.