Heat oil in a large pot over medium-high heat. Cook and stir ground beef in the hot skillet until browned and crumbly, 5 to 7 minutes. Add coleslaw mix and onion; cook for 4 minutes. Add broth, tomatoes, water, brown sugar, lemon juice, and salt.
Bring mixture to a boil, add rice, and reduce heat to medium-low. Cover and let simmer until rice is tender, about 45 minutes.