The technique for this recipe seems a bit strange. The results are great so follow the directions closely. Basically you need to dissolve the sugar with the wine and mint to infuse the mint and sweetness into the wine. Then you are adding the best of the lemon, the zest and the fruit without the pith to make a sweet lemon compote to top the lamb chops.
3/4 cup dry white wine
1/2 cup sugar
1/4 cup (packed) fresh mint leaves
2 Meyer lemons
1/4 teaspoon coarse kosher salt
16 baby lamb chops or 8 3/4-inch-thick lamb chops
2 tablespoons vegetable oil
Combine wine, sugar, and mint in heavy small saucepan. Bring to boil, stirring until sugar dissolves. Remove from heat; let stand 30 minutes. Strain syrup into medium saucepan; discard mint. Using vegetable peeler, remove peel from lemons in strips. Place strips in mini processor. Cut away all white pith from lemons and discard. Working on plate to catch juice, quarter lemons; remove seeds. Add lemons and juice to mini processor; using on/off turns, chop coarsely. Add lemon mixture to mint syrup. Boil until mixture is reduced to 2/3 cup, about 10 minutes. Stir in salt. Cool.
Sprinkle lamb with salt and pepper. Heat 1 tablespoon oil in a large skillet or grill pan over medium-high heat. Add lamb; cook to desired doneness, about 2 1/2 minutes per side for medium-rare. Repeat with remaining lamb. Serve lamb with lemon compote.