Heat grill to medium high. Place 2 martini glasses in freezer.
Place Thyme bunch in a small bowl, pour one cup water over herbs, and soak while preparing lemons.
Cut each lemon into three thick slices. Place sugar on a saucer and swirl to cover bottom of saucer. Press each side of each lemon in the sugar and place on a plate.
Drain Thyme and shake to remove excess water.
Grill lemons for one minute on each side. When lemons are ready to turn, place Thyme on grill and cook for up to one minute, turning once; do not burn. Remove lemons and thyme from grill and cool for five minutes.
Strip Thyme leaves from stem to obtain 1 tablespoon. Place leaves in the bottom of a martini shaker. Press leaves down with a wooden spoon until lightly crushed.
Squeeze lemons into measuring cup and yield 1/8 cup plus 1 tablespoon lemon juice. Add lemon juice to martini shaker, followed by vodka and Amaretto. Place 1 cup ice cubes in shaker. Shake until chilled.
Remove martini glasses from freezer. Place a strainer over each glass and pour half of shaker mixture into glass. Garnish with fresh thyme sprig, if desired.