Place the lentils and water in a soup pot or dutch oven and bring to a boil. Cover, lower heat to a simmer, and cook for about 15 minutes. Add the onion, cummin, and mustard, and continue to simmer, covered, until the lentils are very soft (about 15 more minutes). Add small amounts of additional water, if it seems too thick.
Add the garlic, apricots, and salt, cover, and let sit for another 15 minutes or so. Stir in the vinegar, black pepper, and cayenne to taste (and correct the salt too, if necessary). At this point the soup will keep for several days.
Heat gently just before serving, and serve hot, topped with a few slivers of dried apricot, a drizzle of yogurt, and a sprig of coriander or parsley, if desired.