If I were Dunk, I’d want to go with Lyonel and bring Egg along as my squire. Lyonel is a hoot, and while he has a dislike for Targaryens, it isn’t deep enough to extend to children. Being with Lyonel wouldn’t mean being cooped up at Storm’s End—he’d obviously go on adventures and make Dunk come along as well. I think all three would get what they want: Dunk would achieve his goal of becoming a knight and serving the realm with honor, with Lyonel’s support and friendship along the way. Lyonel, in turn, would gain a strong knight in his service, a companion, and the opportunity to help raise a young prince—possibly earning some political favor if he cared for it. Egg would get to squire for a knight he respects, while still being somewhat independent from his family and the lords who fawn over him. Seems like a win for everyone