In a medium-sized pan, saute onions in 2 tablespoons olive oil over medium high until softened, about 7-8 minutes.
Remove pan from heat and let onion mixture cool.
While onions are sauteing, prepare barbecue sauce.
Combine strained tomatoes, 1½ teaspoons jerk seasoning, 1 tablespoon lime juice, 2 tablespoons honey, and salt to taste in a small saucepan and heat over medium high heat until mixture begins to bubble. Turn heat to low and simmer for about 10-12 minutes.
Remove from heat and let cool.
Brush a stove top grill pan with 2 teaspoons canola oil and heat on high heat.
In a medium sized mixing bowl, combine turkey breast, 1 tablespoon lime juice, 1 teaspoon jerk seasoning, onion and olive oil mixture, and salt to taste. Mix with hands until combined. Do not over mix.
Divide the turkey mixture into four patties.
Place patties on a grill pan and cook for 5 minutes on each side, until internal temperature reaches 165°F when checked with a meat thermometer.
Remove burgers from the grill pan.
Build your burger. Place lettuce leaf on bottom of bun, place burger on top of lettuce, then spoon the amount of sauce you prefer on top of the burger. Top with pineapple slice, 2 bacon slices, and bun top.