Paprika-rubbed steaks with pickled onions

For the onion:
1 small red onion
2 tablespoons fresh lemon juice
2 tablespoons red wine vinegar
1 teaspoon kosher salt
1 teaspoon granulated sugar
4 New York strip steaks, about 3/4 pound each and 1 inch thick
Extra-virgin olive oil
1 teaspoon paprika
1/2 teaspoon brown sugar
1/2 teaspoon kosher salt
1/2 teaspoon freshly ground black pepper

1. To prepare the onion: Cut the onion in half through the root end. Trim off the ends. Slice the onion as thinly as possible and place the slices in a nonreactive, shallow glass dish. Add the remaining onion ingredients and toss together to dissolve the salt and sugar. Set aside at room temperature for about 3 hours, stirring the onion occasionally.
2. Allow the steaks to stand at room temperature for 20 to 30 minutes before grilling. Lightly brush or spray both sides of the steaks with oil. Mix the paprika, brown sugar, salt, and pepper in a small bowl and sprinkle the seasonings on both sides of the steaks. Grill the steaks over Direct Medium heat until the internal temperature reaches 145 F for medium rare, 8 to 10 minutes, turning once halfway through grilling time. Remove the steaks from the grill and allow to rest for 2 to 3 minutes. Strain the onions in a sieve. Serve the steaks warm with the pickled onions on top and mashed sweet potatoes on the side, if desired.