Brine the salmon: Place the salmon in a large ziploc bag. Add cold water to cover (about 2 - 3 cups) along with 1 tablespoon of kosher salt for every cup of water used. Seal the bag and place in the fridge (can be done earlier in the day).
Pre-heat the oven to 400 degrees; place the oven rack in the upper third of the oven.
Drain the salmon, rinse and pat dry. Set salmon on a parchment or foil-lined rimmed baking sheet. Drizzle with a little olive oil and season with salt and pepper. Slice one of the lemons and place the slices on top of the salmon. Bake for 8 minutes, then turn the oven to broil and broil till the lemons begin to char and the salmon is cooked through, about 1-2 minutes more. Remove from the oven and flake into large pieces.
While the salmon is cooking heat 1/4 cup of olive oil in a medium skillet over medium heat. Add the chickpeas, garlic and za’atar and cook at a bare simmer, stirring occasionally, for about 5-10 minutes.
Juice the remaining lemon into a spouted measuring cup – you should have 3 – 4 tablespoons of juice. Drain the oil from the skillet into the measuring cup and whisk to emulsify.
Place the arugula into a medium bowl and toss with just enough of the dressing to coat. Divide between 2 serving bowls, along with the chickpeas, salmon and radishes. Add the charred lemon slices if desired and serve with remaining dressing on the side.