Lodovico is a minor character in this excellent tragedy, and his main role is in Act IV scene 1. However, it is important not to simply dismiss the role of minor characters such as Lodovico, and part of an attentive student's job is to consider how they are used and what function they perform in the play as a whole.
Lodovico then is a kinsman of Desdemona, and he brings news to Othello in Act IV scene 1 that he is to return to Venice, by the order of the Duke, and leave Cassio in command. Lodovico innocently asks after Cassio, which, having heard Iago's suspicions about him, annoys Othello. That it is his wife that responds to Lodovico's question annoys him even further. When Othello strikes his wife because of her happiness at leaving Cyprus, Lodovico is horrified, and this shock is only increased when he accuses her of being a poisonous, unfaithful woman. Lodovico thus acts as a kind of commentary on how Iago has succeeded in changing Othello from the beginning of the play. Note what he says about what he has seen:
Is this the noble Moor whom our full senate
Call all in all sufficient? This is the nature
Whom passion could not shake? whose solid virtue
The shot of accident nor dart of chance
Could neither graze nor pierce?
Such a speech draws our attention to how Othello has become subject to passions that now dominate him, whereas before he was famed for his self-control and his dominance of his passions. Lodovico thus acts as a reminder of how much Othello has changed, and also this event foreshadows the tragic end of the play. It is only one step up from hitting to murder, after all, and Lodovico, like the audience, has observed Othello's anger and murderous passion in this scene.