In a large skillet, cook bacon until cooked through but still pliable. Set aside, then roast jalapeño slices in bacon fat until tender and set aside.
In a clean pan, heat olive oil, garlic, salt, and pepper. Quickly sauté spinach until just warmed, then remove from pan and set aside. Add more olive oil if needed, then sauté oysters until barely heated, about 10 seconds. (Don’t fully cook the oysters at this point because you’ll be cooking them again.)
Preheat a gas grill on low heat. Assemble the oysters: Wrap a slice of roasted jalapeño, one spinach leaf, and a half-slice of bacon around one oyster and secure with a toothpick. Repeat with remaining oysters. Transfer wrapped oysters to grill and cook with lid closed until bacon is crisp, 5 to 8 minutes.
While oysters are cooking, make the aioli: In a mixing bowl, combine lemon and lime juice with mayonnaise and cajun seasoning. Season with salt and refrigerate until ready to use. Serve warm oysters with a drizzle of aioli or use for dipping sauce.