Make mayo: In a bowl, combine mayonnaise, Sriracha, and lemon juice. Chill until used.
Make won tons: Finely chop shrimp. In a medium bowl, combine shrimp, onions, carrot, egg whites, salt, and pepper until well blended.
To assemble won tons, set out about 9 won ton wrappers at a time on a work surface. Measure wrappers: If 3 in. square, spoon a level 1 tsp. filling onto center of each; if 3 1/2 in. square, use 1 1/2 tsp. filling. Using your finger, paint edges of each wrapper with a bit of water. Fold one corner over filling and connect to opposite corner of won ton to form a triangle. Seal edges, pressing out air and squishing filling into corners if needed for fit. Repeat, transferring them as filled to baking sheets lined with parchment paper.
In a 5- to 6-qt. pot, heat 1 1/2 in. oil over medium-high heat to 375° on a deep-fry thermometer. Add about 9 won tons at a time and cook, turning once and adjusting heat as needed to maintain oil temperature, until deep golden, about 2 minutes. Transfer to paper towel-lined baking sheets to drain.
Serve warm with Sriracha mayo.