Cook farro per package directions, then drain, transfer to a large bowl, and toss with 1 Tbsp oil.
Meanwhile, in a bowl, toss onion with 2 Tbsp lemon juice and a pinch of salt. Let sit, tossing twice.
Heat remaining Tbsp oil in a large skillet on medium-high. Season chicken with ¼ tsp each salt and pepper and cook until golden brown, 8 to 10 minutes.
Remove the skillet from heat and stir in remaining 2 Tbsp lemon juice.
Add chicken and any juices to farro along with dill, tomatoes, cucumber, and onion (and their juices); toss to combine. Fold in arugula and feta.
