I used to follow Harvey's protocol, which is just a highly publicized version of natural hygiene, and the point is to have liquids in advance of your meal. Then when you eat to refrain from any fluids until well after your meal. This ensures that you don't dilute stomach acid and other digestive enzymes so your digestion will be efficient.

So then the answer to your question "Are we not supposed to drink anything with a lunch or dinner meal?", is Yes, no drinks with meals.

Yeah, I agree that you're not supposed to drink at meals. Not for Food Combining, and not in general. That's hard, I know, especially if you grew up guzzling down the liquids.
Here are a few options though - just my ideas...

1st of all, I think it's okay to "wean" yourself. Maybe if you only drink one cup (8 oz) per meal for one week. Then, after that, a period of only drinking half a cup (4 oz) per meal. That's mainly to help you swallow something or swish around your mouth, but I don't think it will dilute things significantly, until you can do without.

2nd of all, it is assumed that if you are eating such high water content foods (raw fruits and veggies) and drinking lots of water throughout the day, that you will be well hydrated and won't feel the need to drink.

3rd, this is not the ultimate orthodox Food Hygiene method but in my opinion it is okay to take a small to moderate amount of fresh pineapple or carrot (veggie) juice with some meals. Pineapple, unlike other fruits, won't rot in your stomach, and actually helps the other food digest. And if you want the maximum benefit from your juice you should take it on an empty stomach but if you adore things to drink with a meal it's not like it will be messing up the works. Just don't drink to much, it IS a liquid.

I always wondered about soup... b/c that is "food" but it is SO watery that surely it must dilute everything. Ah well...

And don't forget - food combining or not, if you think you aren't digesting and assimilating your food very well, you should consider taking digestive enzymes with your meal.

Bon Appetite!