Because in the middle of an ongoing civil war with the Blackfyres, Aegon didn’t want to fight one with the Baratheons. Lyonel would definitely fight to the last, and in the Stormlands, that means a half-hundred grinding sieges.
Luckily, Lyonel agreed to a trial by combat.
Also, Aegon V knew that he was sort of in the wrong, even if Lyonel was taking honor to an extreme.
Lyonel Baratheon was rewarded for his failed, bloody (TWOIAF) rebellion with Rhaella. Where the Tullys and Tyrells too weak or too stupid to rebel over Jaehaerys and Shaera?
Aegon V had proved himself so weak, the Reach could have gotten at least all their ports permanently freed of all royal taxes.
The Tullys and the Tyrells hadn’t saved Dunk’s life once.