Haha, ironically, I wished to join the Gotei 13, but I didn't know if I had enough edits. I would be grateful to be your lieutenant, and I am quite surprised that you asked me of all people, but thank you very much :D
Well, basically, we're the police. Anyone violates the policies, or attempts to start trouble, it's our duty to diffuse the situation, and if demanded, I would need to administer blocks. So, mainly our duty should be the diplomatic aspect of the job, which would be to diffuse tense situations before they get out of hand. When they do get out of hand, either I should be notified by you, to block the troublemaker, or Ten, since he is the Captain-Commander. Otherwise, you'd, as Lieutenant, would be working on keeping things leveled. As Lieutenant, you won't need to really report to me anything, and since I'm rather easy-going, unless a user needs to be blocked, you pretty much have free reign in how you go about dealing with troublesome users.