Combine vinegar, sugar, and 1 teaspoon salt in a small saucepan. Cook over medium heat, stirring until sugar is dissolved. Remove from heat and let cool completely.
Slice cucumber lengthwise into long 1/8-inch-thick strips. Cut each strip length-wise into 1/8-inch-wide pieces. Slice the carrot, the jicama and the papaya in the same way. Combine the cucumber, carrot, jicama and papaya in a large bowl. Toss with the vinegar mixture, lemon juice and cilantro.
Bring a medium pot of water to a boil. Add oil, noodles and remaining salt. Boil until noodles are tender, about 2 minutes. Drain and rinse under cold water. Noodles should remain in a bowl of cool water until ready to use.
Before filling the rolls, transfer vegetable mixture to a colander to drain. Gently press out excess liquid. Drain the noodles and arrange on a baking sheet. Cover loosely with a damp towel.
Set up a large shallow bowl of very hot water. Slide a spring roll wrapper into the water. Wrapper will become pliable after about 45 seconds. Remove it from water and lay it flat on paper towel. Place lettuce on the bottom half of the wrapper. Arrange a 1/4 packed cup of vegetables over the lettuce. Spread out 1heaping tablespoon of noodles over the vegetables. Roll wrapper up, tucking in the ends as you go. Roll as tightly as possible.
Repeat with remaining wrappers. Trim off the ends of the rolls. Cut each roll in half and each half in half on a diagonal. Stand rolls on the flat end to serve. Serve with peanut sauce.