Grate 1 tsp. zest from the grapefruit. Using a small sharp knife, cut off the peel and white pith. Working over a medium bowl, cut between the membranes to release the segments into the bowl. Squeeze the juice from the membranes into the bowl. Cut the segments into bite-size pieces. Transfer 3 tbsp. grapefruit juice to a small bowl. Add the onion and lemon juice; season with salt. Let stand for 10 minutes.
Meanwhile, in a dry small skillet, toast the nuts over medium heat, stirring often, until fragrant, 5 to 7 minutes. While the nuts are still hot, in a small bowl, toss with 1 tsp. oil and a generous pinch each of salt and pepper. Let cool, then coarsely chop.
Wipe out the skillet, add the coriander and cumin seeds, and toast over medium-low heat, shaking the pan often, until fragrant and slightly darker in color, 2 to 3 minutes; let cool. Transfer the seeds to a cutting board and crush with a heavy skillet.
Whisk the remaining 2 tbsp. oil into the grapefruit juice. Whisk in the sugar, a generous pinch of pepper, and the crushed spices. In a large bowl, toss the beets, green beans, frisée, baby greens, the reserved grapefruit segments, half of the nuts, and the dressing; season with salt and pepper. Arrange the salad on a platter. Drizzle with the remaining dressing, then top with the remaining nuts and the grapefruit and lemon zests