In a blender or food processor, blend tomatoes, onion, garlic, cilantro, sugar and salt until well blended.
In medium skillet, heat oil. Add tomato mixture and bring to a boil. Reduce heat and simmer for 5 minutes. Remove tomato sauce from heat and cool. (Sauce may be prepared 2 days ahead and refrigerated.)
On a cutting board using a long, thin-bladed, sharp knife, cut each brick of cream cheese lengthwise into 4 strips. Arrange a bed of lettuce on an oblong platter.
Place two cream cheese strips together at their narrowest ends. Top cream cheese with avocado slices and a thin layer of tomato sauce. Repeat layering three times. Make a second stack alongside the first. Pour remaining sauce over the top.
Serve at room temperature. Surround with tortilla chips and serve with a knife to slice through layers and spread on chips.