As Kaj replied in yesterday's thread on the topic - he is waiting for the user's response, and if he doesn't get one he will likely ban(or take another action against) the user in a week.

At any rate, why did you decide that there is a need for yet another post on the topic so soon (doing it after the week is over would've made more sense to me)? I was going to be charitable and assume that you haven't seen his response or something of the sort, but you've replied to that very comment.

Moderators (in the technical sense) can't do anything, there are no tools presently available in forum's software to solve the issue (other than "manually" examining LW's database, which is not public). A starting point could be to make a ticket on LW's issue tracker detailing the problem and possible solutions. (I found two tickets on the issue, one from Nov 2012 with some discussion, another from Jun 2013 reporting an attack.)

A possible solution is to make available to moderators the following views for each user: "top downvoters", "top upvoters", and a mode where one can see who voted how on each comment of that user (perhaps with all of these able to focus attention on votes cast in the last N days, or in a given time interval, that is "top downvoters in last N days", and seeing which comments were voted on how by whom in the last N days). A list of users who accessed the forum from the same IP address as a given other user could also be useful, to detect sockpuppets. Then, there would be some data that moderators can use to investigate claims of abusive downvoting.

Additionally, even if a responsible party is discovered, there needs to be a way of stopping them, which currently there isn't (moderators can't personally ban users, only remove specific comments and posts). Possible measures are disabling a user's voting ability, or disabling the ability to vote about a particular other user.