I wish there were a simple answer. Some Lyme disease sufferers can't have ANY grains, gluten or non-gluten. For those that can at least tolerate non-gluten grains, however, I have a suggestion for a great carb to add to your list.
I know, doesn't oatmeal contain gluten? You ask. Yes, but if you special-order it from a company that grows, harvests and processes oats separately, so that they don't get cross-contaminated by wheat, rye or barley, then you can get away with it. Is this costly? Yes, but so is losing your sanity.
Of late, I have been having gluten-free oatmeal for breakfast, sprinkled with cinnamon and stevia on top, and boy, are my taste buds ever happy! It's been a long time since I could regularly eat a food I really adore. I tried "regular" oats before special-ordering my gluten-free ones, hoping the amount of gluten in the regular oats would be minimal, but they left me fatigued, so I was amazed when my new, gluten-free oats actually gave me more energy!
If you can tolerate rice or other non-gluten grains such as quinoa, why not try non-gluten oats, as well? Oats are rich in fiber, (our guts need fiber!), magnesium (what mineral more needed by Lymie's is there than magnesium?), tryptophan (ah yes, the precursor to serotonin! What a great fix for depression!), selenium (a co-factor of glutathione, which is important for liver detox and other functions), manganese (also helps depression!) as well as other antioxidants. Oats also stabilize blood sugar and reduce cholesterol. For Lyme sufferers with severe adrenal fatigue (that's most of us!), stabilizing blood sugar helps the adrenals.
Two sites selling gluten-free oats are: www.food4celiacs.com, and www.bobsredmill.com.
So try some horsey feed, and see if it doesn't give your body and mood a lift, in more ways than one.