For dressing: Puree first 5 ingredients in blender. Let mixture stand at least 15 minutes and up to 1 hour. Strain mixture into small bowl, pressing on solids to release any liquid; discard solids. Stir in sweet chili sauce. (Can be made 1 day ahead. Cover and refrigerate.)
For tofu: Combine first 7 ingredients in large bowl. Add tofu and dressing to bowl; toss to coat.
Arrange 1 or 2 lettuce leaves on each of 6 plates. Divide tofu mixture among lettuce leaves and serve.
*Available in the Asian foods section of most supermarkets and at Asian markets.