Its really hard to effect the relationships between two NPCs, and to my knowledge there is no mechanism in the game to effect this beside an occasional random quest. But here is some of the things you can do. The first thing you need to know is what kind of Lord is this NPC. If he is Honorable he may never leave his king unless the faction is on the verge of elimination. If he is on the other spectrum and Debauched he will more than likely go to the faction that gives him the most opportunity for lands.
So you want to rebel and have lords join your faction, you will need high Right to rule (send companions out to get this) and free unassigned fiefs that attract other Lords. If you are trying to convince a lord in the field to join you, you will need to have a high relationship with him (based on quest, saving him in battle, etc.) and High persuasion skill. However this wont be enough, this NPC Lord will need to have a low relationship with the King and the faction will need to be in decline, but most important the Lord will have to be less than Honorable like I mentioned previously.
The best case to have what you want to happen is for you to rebel from a small declining faction where the NPC lord you are trying to convince is debauched, and has really good relationship with you, he has no fiefs and you have unassigned fiefs already. Still however it probably wont happen. Your best bet is to wait out the good lords who are not debauched and quarrelsome, these are the ones besides your companions that will maintain good relationships with you. Eventually that lord will join you if you maintain a good relationship with him and you continually try to convince him over time, you just need all those other things in place as well.
Hope this Helps.
Arcade Knight