Place the andouille sausage into the bowl of a food processor, and process until finely ground; transfer to a large bowl.
Add in the ground chuck and Cajun seasoning; mix just until combined (do not overmix).
Form into six equal-sized patties, slightly larger than the sandwich rolls.
Slightly press down and form an indentation in the center of each patty.
Set patties aside.
Prepare the Bayou Sauce:
Place the mayonnaise, ketchup, mustard, Sriracha, garlic, capers, lemon juice, parsley and salt into a medium bowl, mix to fully combine; set aside.
Prepare the Drunken Onions:
Place a large heat-proof skillet onto the grill (or side burner over medium-high heat).
Add in the butter, allow to melt.
Add in the onion and salt and cook until onions are softened and lightly browned, approximately 10 – 12 minutes.
Remove the skillet from the heat, add in the beer, and place skillet back over medium-high heat.
Cook until beer has been absorbed, approximately 5 minutes.
Set onions aside.
Prepare the Buttery Bayou Crawfish:
Place a medium heat-proof skillet onto the grill (or side burner over medium-high heat).
Add in the butter, allow to melt.
Stir in the crawfish; mix in the Cajun seasoning and cook until crawfish is heated through, approximately 2 – 3 minutes.
Toss in the parsley.
Cook burgers:
Brush the grill rack with vegetable oil.
Place the burgers onto the grill and cook until done to preference, approximately 4 – 5 minutes on each side for medium.
During the last 2 minutes of grilling, top each burger evenly with the cheese, as well as place the rolls, cut side down, around the edge of the grill to toast lightly.
To assemble the burgers:
Place bottom portion of rolls, cut side up, onto work surface.
Top each evenly with the onions, then a burger, then evenly with the crawfish and shredded lettuce.
Evenly spread the bayou sauce onto the cut side of the roll tops, place onto burgers, cut side down.