Lyle left the hideout after the entire fiasco with Luna had finished. Iodel and Ulon would escort Harrison to the Rain family mansion and they would then go back to where they were staying, while Harrison would deal with Luna together with his family.
He had luckily managed to show enough power during the battle to keep his real strength still a secret. Even though he didn't do much, neither did Silver thanks to the fact Luna was boosting her power to the maximum with demonic energy and was as powerful as a high-grade Golden Knight, which was enough to defeat two low-grade Golden Knights usually.
Plus, all of them knew that Lyle was an assassin, a person that was at his strongest not when fighting head-on, but when silently sneaking around and taking the opponent unaware. It was thanks to all of that that Lyle's strength was still alright as Elena and the other two guards had been unable to do anything to Luna.