Bring the water, lemons, onions, and garlic to a rolling boil.
Boil uncovered until reduced by half, at least thirty minutes.
Strain the liquid. If it has over-reduced, just add some water back to get it up to a quart of liquid, and put it back into the pot.
Add the tomato puree, vinegar, sugar, Worcestshire, salt, and pepper.
Stir to combine and bring back to a boil for about five minutes until everything is throughly incorporated.
Use immediately, or let it cool then place in refrigerator. Makes two quarts of sauce.