Place 1 Tbsp oil on the skillet and heat over medium-high heat.
Add the chicken drumsticks and cook for about 10 minutes on each side (or until they are 80% cooked).
While the chicken is cooking, slice or cube the acorn squash.
When the chicken is about 80% cooked through, set aside and add another tablespoon of oil to the skillet. Cook the squash for about 5 minutes, flipping half way through.
Add the chicken back into the skillet. Place the entire skillet in the oven for about 20 minutes or until the chicken is completely cooked.
Remove from oven. Add in the arugula and squeeze lemon over the entire dish. Serve and enjoy!