In a pot of boiling water, cook the lobsters for 6 minutes. The meat should not be cooked all the way, only about 75 percent done. Cool and remove the meat from the tails. Dice into 1-inch pieces. Reserve the rest of the lobster meat for another use. Mix the tail meat with the citrus juices and refrigerate for 1 hour.

Add the celery, jalapeno, cucumber, arugula and onion to the lobster and let stand another 30 minutes.

Heat the oil in a grill pan over medium-high heat. Grill the radicchio until just wilted, 2 to 3 minutes per side. Season with salt. Slice the radicchio into coarse ribbons. To serve, make a bed of radicchio and spoon the ceviche right on top.