Place chicken between 2 sheets of heavy plastic on a solid, level surface. Firmly pound with the smooth side of a meat mallet to 1/4-inch thickness.
Place flour in a bowl. Beat eggs together in a separate bowl. Mix crushed oat cereal, garlic powder, salt, and black pepper together in large resealable plastic bag.
Dredge each chicken breast in flour and dip into eggs, allowing excess egg to drip back into bowl. Transfer coated chicken to cereal mixture; seal bag and shake until evenly coated. Place coated chicken on a plate and refrigerate for 1 hour.
Heat oil in a 12-inch skillet over medium-high heat; fry chicken until browned, 3 to 4 minutes per side. Transfer chicken to a paper towel-lined plate and squeeze lemon over each.