You must first take server-side action to block the content from being syndicated to a LiveJournal account. For instance, if the syndicated account on LiveJournal is using your site's RSS or Atom feed, you could either disable that feed or block LiveJournal's IP addresses (126.96.36.199/30) from accessing your server. Either will prevent your content from being syndicated onto LiveJournal.
Syndicated accounts retain entries for two weeks to allow LiveJournal users time to view them; after that period, the entries are automatically deleted on the next update. Content may continue to be visible on the syndicated account after you have disabled access to the feed, but there is no way to accelerate the automatic deletion process.
LiveJournal will not take action if the syndicated account is using a feed provided by your site. However, if you are unable to disable the feed or block LiveJournal's IP address, you should contact the LiveJournal Abuse Prevention Team
for further assistance. Similarly, if your site does not offer a RSS or Atom feed, but the content is being "screenscraped" and syndicated onto LiveJournal, please file a report with the Abuse Prevention Team.