Make the jerk sauce: Whisk the lemon juice, olive oil, jarred jerk sauce, Cajun seasoning and red pepper flakes in a bowl until combined. Stir in the bell pepper, jalapeno and garlic; cover and refrigerate overnight.
Make the vegetables: Heat a large skillet over medium-high heat and add the olive oil. Add the carrots, zucchini and bell pepper, season with salt and cook, tossing occasionally, until slightly softened, about 5 minutes. Add 1/4 cup of the prepared jerk sauce and cook until the vegetables are glazed, 1 to 2 more minutes. Remove from the heat and cover to keep warm.
Grill the burgers: Preheat a grill to medium high and brush the grates with canola oil. Form the beef into four 3/4-inch-thick patties and season generously with salt and pepper. Grill about 4 minutes per side for medium rare. Meanwhile, lightly toast the buns on the grill.
Serve the burgers on the buns; top with the sauteed vegetables.