Non-alcoholic substitution for dry white wine in bolognese sauce and other tomato sauces?
White wine in tomato sauces adds:


Some acidity, but tomatoes are quite acidic as well
A touch of fruitiness and flavor
Alcohol, which does not all cook off, which can enhance the perception of the dish due to some flavor molecules being alcohol soluble, especially in tomatoes


Since you are avoiding alcohol itself, some of the options you might use are:


Simply omit the wine.   The dish may not be quite as good, but it will still be good.
Use a splash of verjuice (un-fermented grape juice) if you can get it; this will give you some of the fruity and acidic qualities, without the alcohol.
Use a splash of white wine vinegar (unless you are concerned with the trace amounts of alcohol that may persist from its production); this will give you some acid, but you are not likely to use enough to add any significant fruitiness.


Since you are specifically avoiding alcohol, you necessarily lose the flavor enhancing effect it can have, but a good well seasoned dish will stand up without it.

I would suggest you make your sauce, and if you feel it lacks brightness, to try cooking down a little white wine vinegar or apple cider vinegar and adding it; otherwise, leave it alone.

And of course, taste as you are cooking to season it well.

Again, as one component of several in a lasagna, which is all about the integration and balance of all of the components, I wouldn't worry about it this overly much.