LLOYDYuan catches on quickly that Lloyd and his gang will be a good pawn in order to accomplish the goals of the Renegades. He starts off introducing himself and helping Lloyd save Colette, simply because he doesn't want Colette to become the vessel for Martel. When Yuan convinces Lloyd and gang to go to the Temple of Lightning to form a pact with Volt, Botta and Yuan stand outside and wait. Yuan comments that if things get too tough they will go in and help, but he is testing out Lloyd's skills because he is Kratos' son. After the pact is formed, Yuan asks Lloyd if he loves and wants to meet his father, which Lloyd obviously agrees, but says only after Colette is saved will he seek his father out. Yuan is quick to turn his blade to Lloyds life when Kratos appears, telling him to release Origin or else Lloyd dies. Lloyd is surprised by this request, wondering why Kratos would care about his life so much... just to find out that Kratos is his father from Yuan. An explosion happens, and Yuan is thrown away from Lloyd. Lloyd is saved by Kratos here, and Yuans plan is spoiled. However, after seeing the true mental and physical strength of Lloyd, Yuan starts to realize that Lloyd could be the answer to his problems, but not just as a pawn. Yuan comes for Lloyd and Kratos once more, but this time ends up fighting Kratos, both ending up extremely injured. Kratos wonders out loud if Lloyd will be able to save the world with the hope he has, similar to what Kratos and Yuan once had. Yuan states, "Shall we go find out the answer," implying that he finally has hope that Lloyd and Colette will be able to do what they were too late to do.
Lloyd is a special character for Yuan because he helps Yuan's character to grow again. Lloyd resembles hope for Yuan. He is the light in the dark that Yuan was subconsciously searching for. Lloyd and his group are a lot like Yuan, Martel, Mithos, and Kratos back in the day, before everything went wrong. I think that it is important to notice that Yuan admits to giving up hope, but he is able to find it again thanks to the words of Lloyd and Colette. He sees a lot in them that he saw in his own group. I think that is the main reason they emphasized this relationship in the OVA to show the comparisons between Yuan and Lloyd, and how Lloyd almost saved Yuan.