How do I persuade people?

Unfortunately I can only answer based on my hours and experience with Mount and Blade: Warband. Hopefully most of this can adapt.

Firstly, three persuasion isn't a whole lot. Try getting it at least above four, I'd say. I usually try to level up the Charisma skills (leadership, trading, persuasion, etc) before any others, including strength, as Charisma is such an important part of the game.

Secondly, and this is probably more relevant, all lords have different personalities. This means that some are less likely to be persuaded than others.

Thirdly, it should also depend on your relationship with them. A higher relationship means it is easier to persuade them, and sometimes with a high enough relationship you might have special options (such as to make a sacrifice because you two have a great relationship, but this may drop relations. I'm also not sure if this occurs in the original M&B).