The quickest answer would be to say that indeed Lakshmana would have seen it as his duty to intercept an arrow meant to kill Vibhishana. Certainly, Lakshmana is bound to serve Lord Rama. He feels that his only duty is to be a servant to him. Lakshmana also recognizes fairly quickly that Vibhishana has gone to great lengths and sacrificed much to be in Lord Rama's service. Assisting him in battle is a demonstration of loyalty that the very embodiment of loyalty, Lakshmana, would honor. When the arrows are meant to kill Vibhishana, Lakshmana is probably overwhelmed with the reality that he could not stand by and watch a devotee of Lord Rama be killed. It would be a sin to have to tell Lord Rama that he was able to stop one of his devotees from dying, but did not do so. It is for this reason that Lakshmana willingly takes these arrows. Lakshmana views his being as one that is totally dedicated to Lord Rama. This also means that all of the devotees of Lord Rama are also served through Lakshmana's loyalty and thus, taking the arrows makes sense.