Luckybackup log files are saved in - home/yourusername/.luckyBackup/logs - . However, if luckybacup is freezing your machine it probably doesn't have time to write a log which is why you can't find one.
How about asking on the luckybackup forum?http://sourceforge.net/p/luckybackup/discussion/
One thing that springs to mind though is if you are trying to backup anything other than your home folder you will probably need to run it as root (ie use sudo).
Fujitsu Lifebook AH532. Intel i5 processor, 6Gb ram, Intel HD3000 graphics, Intel Audio/wifi. Realtek RTL8111/8168B Ethernet.Lubuntu 13.10,Ubuntu12.10 (Unity), Mint16 (Cinnamon), Manjaro (Xfce).