To be considered for vassalage, you need substantial renown (typically 150-200+) and a good reputation with the king of your chosen faction. Continue to fight for your mercenary contract, win battles, and complete quests for lords. Your renown increases with every victory, especially against larger armies. Participating in tournaments also grants renown.
Honor is another important factor. You gain honor by performing honorable deeds, such as refusing payment for rescuing a lord, or releasing captured lords after battle. Avoid dishonorable actions like looting villages or attacking unarmed peasants, as these will decrease your honor and make it harder to become a respected lord.