How hard will it be to ask for no salt and no lemon or vinegar on foods in Rome, Venice, and Tuscany? I am on an alkaline diet
Are you asking about extra salt, lemon, etc. on the foods like salads or are you asking about dishes/sauces being prepared salt, lemon, vinegar free? The latter would be far more difficult to achieve. I have never heard of an alkaline diet. Is it medical or choice? Lemon and vinegar are acidic but salt is not.
It will be very difficult. Even if there were no language barrier (if you spoke fluent Italian), the concept of food customization does not exist in Italy, or most of Europe. In America, it's common for diners to make requests, and restaurants are used to this and honor them. "Dressing on the side," "No bacon on the salad," "French fries instead of hash browns," etc. In Europe, the dish is the way it is. If you don't like the dish as is, you are supposed to order something else. Someone posted the same experience with allergies - the staff at the restaurant was eager to help them choose suitable dishes from the menu, but there was no option to modify dishes to make the suitable. Avoiding vinegar shouldn't be too hard. Lemon is often served on the side, for you to squeeze fresh over your dish, so you can easily avoid this. But many dishes will have some salt (not the huge amounts sometimes used in the US). If you are on a very strict diet (for instance, if even small amounts of salt will be a problem), you may need to rent an apartment and prepare your own food.
Lemon juice is often added during the cooking process for fish and some meat dishes. If you see the words "al limone" or "al aceto" (vinegar), avoid those dishes. If you want to ask if the item is free of these substances, ask "Senza limone?" "Senza aceto?" "Senza sale (salt)?" Keep in mind that salt is added to boiling water for cooking pasta, and pizza dough usually has salt in it (as do most breads, although there are some regional breads that are made without salt).
The power of the web. Found the alkaline diet. Not medically related. Looks like it is mostly vegetarian with emphasis on certain vegetables and non-processed foods. You will be fine. When ordering salad in Italy, generally it is not the mixed variety of mostly lettuce as you find in the states. It will come on a plate with with each salad item in a little pile. Corn is very common. Prepared salad dressings - blue cheese, Thousand Island, etc., - are almost unknown. Each table will have a bottle of vinegar and olive oil so you can dress the salad by yourself or not. Obviously pasta, sauces, etc., are off your list so you will not even have to ask about the acidic content. Unfortunately you are going to miss one of the great reasons for going to Italy - the food.
How much salt is there in gelati? Can't be very much, if any. I could handle a gelati diet :-)