Cook ground beef in a skillet over medium heat, breaking the meat up as it cooks, until beef is browned and crumbly, about 10 minutes. Drain excess grease and stir in taco seasoning mix. Remove from heat and let stand until beef mixture is cool.
Mix ground beef with Cheddar cheese, ranch dressing, Italian dressing, and red onion in a large salad bowl. Chill the beef mixture until cold, at least 30 minutes. Lightly mix in lettuce and tortilla chips just before serving.
