Thinking about how Lucius most likely saw that time Liko and Amethio were stuck in a cave together via Zygarde, since he knew everything about what the RVT and modern Explorers were up to through Zygarde. And unlike Gibeon he full-on heard everything Liko and Amethio talked about there.
Gibeon saw footage of them together back then and lashed out in anger. It's pretty obvious in hindsight his anger was from a place of hurt over what he once had with Lucius and how much it hurt him that their time together ended on such a sour note. He knew Liko was Lucius's descendant. When he saw that he most likely saw himself and Lucius and the friendship they had. Despite everything Gibeon held Lucius close to his heart. Lucius was his best friend, and he cherished the bond they had. He carried on the name Explorers, even though Lucius was the one who coined it for them and Rystal. He kept bringing up Lucius in private and how "their adventure isn't over yet". So seeing Amethio and Liko on friendly terms stung for him because it reminded him of what he and Lucius once had between them and how deeply it hurt him that he didn't have that anymore.
On the other hand Lucius saw everything and even heard what the two of them talked about. Liko said flat out that there's stuff you will never know if you don't hear people out. And I think that resonated with Lucius and made him realize what went wrong between him and Gibeon for things to end that way. Because when they did see each other again in Laqua, Lucius didn't hold it against Gibeon when he kept saying Lucius and Rystal "betrayed" him, and how he kept saying Lucius couldn't understand him. He admits they should've talked more. Talked to each other about their dreams and ideals. And he even apologized that he didn't. Seeing what Amethio and Liko talked about in that cave probably made him realize that. If only he and Gibeon had truly opened up to each other and talked to each other, things wouldn't have gone that way.
Gibeon and Lucius's bond was so tight that even 100 years later and despite what happened in Laqua that day it still persisted. They still held each other close to their hearts. They expressed it in different ways but both of them deeply wished things didn't turn out that way. They were truly at peace when they were able to reconcile before they passed on. But what they saw with Liko and Amethio is what they once were, only they have the potential to be better than they were, as they carve their own paths forward.
