Combine cucumber and vinegar in bowl; set aside.
Combine mayonnaise and Sriracha in second bowl; set aside.
Combine soy sauce, sugar, garlic, and oil in third bowl.
Cook beef in 12-inch nonstick skillet over high heat until any juices have evaporated and beef begins to fry in its own fat, 8 to 10 minutes.
Add soy sauce mixture to skillet and cook until nearly evaporated, about 2 minutes.
To serve, fill lettuce leaves with beef mixture and top with pickled cucumbers and Sriracha mayonnaise.
