I am not entirely sure this is really a bicycle question. It amounts to "I can't eat my usual lunch while riding a bike. What should I do".
Fundamentally you can take two different approaches. First, you can modify your bike or riding style so the food you currently eat works. The most obvious solution is to fix the bike in place and add a table to the front. An exercise bike, in other words. Mounting a table to the front of a moving bike wouldn't help much, as road vibration and wind would make it less useful, you would probably want a bin or bucket instead.
Secondly, change the food. This is what most riders do. Eat things that are either fluids, or non-messy finger foods. By attaching a small bucket to your handlebars you could eat most potato chip style foods, or kebabs or even fish and chips, "buffalo wings" or similar. Fluid foods are more commonly associated with athletes, though, because they require less effort to digest. Mostly those are powders that you mix with water and put in a drink bottle. They tend to be focussed more on content than taste, though, and are often "edible" rather than "nice to eat". The opposite of most takeaway food, in other words.
Finally, eating while exercising is not really a great idea. To get most benefit from exercise you need to be working fairly hard, which means breathing through your mouth. It's hard to do that while eating, and it's not safe - you could easily choke. Your body will struggle with the competing demands from your legs and stomach, because digesting food is an energy-intensive activity. You will cramp more easily, and will find it generally hard going.