Cover lamb with cold water; squeeze in juice from 1/2 lime (adding rind) and add a few pieces of the chopped onion. Let sit, stirring every so often, until water is very pink and cloudy, about 10 minutes. Drain well, discarding the lime rind.
Meanwhile, toast chiles in a large frying pan over medium heat, turning as needed, until fragrant and starting to darken, 6 to 8 minutes; when cool enough to handle, remove stems. Put in a food processor with remaining onion, the garlic, cloves, thyme, cumin, vinegar, 1 1/2 cups broth, and the salt. Whirl together to make a thick sauce, adding a little more broth if needed.
Combine sauce with lamb and bay leaves in a large, wide dutch oven, mixing to coat and spreading evenly. Bring mixture to a boil over high heat, then reduce heat, cover, and simmer, stirring occasionally, until lamb is very tender when pierced, about 2 1/2 hours. Cut remaining 1 1/2 limes into wedges and serve on the side, along with Cilantro Rice.
HANDS-FREE METHOD: Once sauce and lamb are mixed in the dutch oven, bake about 3 hours in a 275° oven.
*Find the chiles in well-stocked Latino markets.
Wine pairing: Ceja 2009 Syrah. This pungent lamb needs a dark, meaty red wine. The Ceja Syrah has a matching earthy soul from its cool-weather vineyard site.