In 1-gallon resealable food-storage plastic bag, mix oil, lime juice, grill seasoning and 3 teaspoons of the Sriracha sauce. Add chicken; seal bag and turn to coat. Refrigerate 1 hour to marinate.
Spray grill rack with grilling spray. Heat gas or charcoal grill. Remove chicken from marinade; discard marinade. Place chicken on grill over medium heat. Cover grill; cook 12 to 14 minutes, turning once, until juice of chicken is clear when center of thickest part is cut (at least 165°F). Cool slightly; chop chicken.
To assemble tostadas, spread refried beans over tostada shells. Spread guacamole over beans. Top evenly with chicken and cheese. Stir remaining 1 teaspoon Sriracha sauce into taco sauce; drizzle over tostadas. Place tostadas on grill. Cover grill; cook 2 to 3 minutes or until cheese is melted. Top with lettuce. Serve immediately.