You need to protect yourself when you're on the web. Even if you tend to stick to secure websites, you never know when a virus will sneak in. This is why we rely on anti-virus software in order to stay safe and keep our computers running like new no matter how much browsing we do.
LUE - Norton LiveUpdate Log File is the file type used by Symantic security software in order to keep track of updates made to the platform. Most anti-virus programs keep a database of known viruses and malware in order to identify them when they show up, sort of like your immune system identifying a common cold virus that it has already kicked at some point in the past.
The LUE files are divided up into two seperate sections: TempLog.LUE for temporary information pertaining to the updates, and Log.LUE, which is a permanent log of all of the viruses and malware updates that you have received. In any event, don't delete or alter either of these, just let your antivirus software do the work in regards to the LUE files. The LUE files simply help your antivirus software to know which files are safe and which are not. Simple as that.