I also use to have an heartburn problem. But I did not blame the acidity but the contents of fats one has problems digesting. I changed a few things and watch what I eat. With a lasagne the problem my be in two areas. First, the cheese, and secondly the meat. Also for some people the tomato acid may be a problem as well. However, try the following:
Your meat, use a lean beef mince, it may be a bit more expensive but better. When you fry off the mince for your bolognaise sauce, use olive oil, not to much. Olive oil is good for you and in a bolognaise, it tastes great. I also dice onions, garlic, fine diced carrots, fine diced leak and fine diced celery in my bolognaise. A touch of tomato paste for the thickness of the sauce and either beef stock or diced tomatoes and water. Seasoning and fresh rosemary or basil. Some people prefer Italian herb mix.
Be careful with to much cheese. Cheese has usually a very high fat content and used in moderation it should not cause indigestion. Instead of just cheese, I make a white sauce and add a bit of grated parmesan in to it. My white sauce I use milk, bring milk to near boiling point, add a runny paste of just white flour and cold milk to the hot milk and stir well while you bring the sauce to the boil again. Add some grated Parmesan cheese. Parmesan cheese has not a very high fat content.
Pasta, I simply use instant lasagne sheets. One layer of instant lasagne sheets, bolognaise sauce, a touch of my white sauce, one layer of instant lasagne sheets again and so forth. At the top I use the rest of my bolognaise and covered with the left over cheese sauce. To finish I sprinkle fine grated Parmesan or tasty cheese. Bake in the oven until ready. Now I make it a habit to have a nice green salad or mixed salad with my lasagne.
My hearth urn was always caused from indigestion and then I realised that I had something really fatty, like a meat pie.
Now I avoid Serbian foods with high fat content and I can not remember when I had my last heartburn. The combination of fats and tomato acid may intensify the problem of heartburn.
Now here is one more tip for you. You can enjoy tomato sauce for your pasta. When you cook a tomato sauce and you want to take the acidity out of the sauce, try this:
In a seperate small saucepan put about 50 ml of black Balsamic vinegar and about 4 tablespoons of brown natural sugar. Bring it to the boil, mix well until the sugar is dissolved. Add the mix to your tomato sauce. Add a bit at the time and try your sauce. It kills the acidity and it enhances the taste.
Now, you may ask, why Balsamic vinegar, has acid as well. That is correct, but it is a different acid, which is good for you. You can call it alkaline instead of acid. With the sugar it works like a dream in your tomato sauce. By the way, a very good Italian chef thought me that trick.
I hope that I could shed some light in to your heartburn problem.
Cheers and enjoy.