Fill a 2-quart pitcher 1/4 of the way full with ice.
Pour in all the cherries and syrup, lime juice, simple syrup, and lemon-lime soda. Stir to combine.
Pour into glasses over ice. Garnish with a cherry and lime wedge or slice.
Notes
If you know that you won't have time to juice the limes, you could substitute limeade concentrate instead. Add about 1/2 cup of concentrate instead of fresh juice. Then mix everything is mixed together and taste the drink to see if you need more lime flavor. Pro Tip: If you're using limeade, wait to add the simple syrup. Since the limeade is sweetened, you may not need as much or any syrup to balance out the drink.
Soda does go flat after a while so don't make a pitcher of copycat Sonic cherry limeade too far ahead of time.