To a small mixing bowl, combine 2 tbsp olive oil (reserve 2 tbsp for searing), lime juice, and cajun seasoning. Mix well. Remove salmon from packaging and pat dry with paper towels. Place into a large, glass Pyrex dish (flesh side up if not skinless) and brush the marinade over each one. Cover and allow to marinate on the counter for 30 minutes. *SEE NOTES BELOW
While you're waiting, prepare the rice and avocado salsa. Combine all ingredients for the salsa into a medium-sized mixing bowl and cover. Place into the fridge until ready to use.
Add the rice to a fine mesh strainer and rinse thoroughly under cold water for 1 1/2-2 minutes until the water runs clear.
In a medium-sized stockpot over high heat, bring the water and salt to a boil. Add the rice and lime juice and stir well to combine. Allow it to return to a low boil, reduce the heat to low, and cover with a tight lid. Cook for 15-20 minutes (follow instructions on package), or until all liquid has been absorbed by the rice. The rice should be tender.
Remove from heat and allow the rice to steam in the pot for another 5 minutes - undisturbed. Just before serving, fluff the rice with a fork to separate and add in the chopped cilantro. Taste test and adjust salt and lime juice to your liking.
Heat a large cast-iron skillet over medium-high heat with the olive oil until hot. Place the salmon filets flesh side down, pressing them gently to ensure that all of the filet is being seared. Sear, untouched, for 3-4 minutes per side or until crispy.
Optional: Squeeze 1/2-1 full lime over all of the filets after you flip. Continue to cook the salmon until it reaches desired doneness. Taste test and adjust salt and pepper, as desired.
Serve filets over rice and garnished with the avocado salsa.