I don't have diabetes but have read a lot about dieting and losing weight. One of these reads took to me to article that mentioned diabetes.
It mentioned the key to better managing diabetes is losing weight. And the best physical activity to lose weight are aerobic or cardio vascular exercises and cycling is one of them.
How you ride your bike will also factor in. If you're on low-carb diet, the majority of your rides should be easy but still long enough. If you're familiar with the '5 heart rate Zone or exercise intensity, out of 5, you should spend most of your rides at Zone 2 for long periods. Like at least one hour of Zone 1 to Zone 2 a day and if you can't always ride your bike outside, consider investing in smart indoor bike trainer.
Also use a heart rate monitor if you haven't already. Zone is 60 to 70% of your max heart rate and considered light or low intensity effort. If you know your max heart rate, there are two ways to know your max heart rate, you can do an all out sprint (Zone 5 effort) for 30 seconds and note your heart rate or use the formula 220 - (your age). The formula is a rough estimate and the sprint will typically give more accurate result.
Why not put more time in more intense Zone 3 and above? These zones will much more rapidly use up the glycogen energy stores in your body. Glycogen ultimately comes from carbs and if you're on a low carb diet, it will cause you to fatigue much sooner and hamper efforts to maximize fat burning which occurs at Zone 2.
Eventually, you may get faster at riding your bike as your endurance improves and you get stronger, that's OK as long as the effort remains light and you remain at Zone 2 heart rate. Do note as you get more physically fit, your max heart rate might change. It will likely get lower.
And here's takeaway, you can still do weightlifting in the gym but this doesn't mean you let go of cycling. You cannot sacrifice the time you spent on cycling because the aerobic, fat-burning nature of cycling still makes it more important exercise than weight lifting.
And weight lifting may not agree with your low carb diet. Weight lifting will not only raise your body's demand for protein but carbs as well. Fortunately, there's a solution. You may increase your carb intake if adding weight lifting to your routine but make sure you eat low Glycemic Index carbs (examples like green vegetables, most fruits, raw carrots, kidney beans, chickpeas and lentils) to prevent blood sugar spikes.
Weight lifting might complicate things but it comes with benefits. It builds muscle mass and more muscle mass improves fat-burning even if at rest. And having more muscles helps minimize muscle atrophy as you age. However, despite it, cycling still remains your best option to lose weight and fat. Brisk walking is also good. Running, not nearly as good due to higher impact strain on the joints.
And if you drink or eat anything while riding your bike will also matter. Water is fine, electrolytes is fine. But anything with lots of sugar or High Glycemic index ingredients would be terribly bad like Gatorade and many examples of energy bar and energy gels.