Question: I'm using Lubuntu 11.10. Every time I shut down I can read FAIL in red letters, but I can not read more. 

So, how to read the log messages and try to solve the problem?

Answer: 
Like Graeme said, with ro or dismounted filesystem, killed klogd there is no way 
to write such info to a file. A solution may be using a console ( serial port ) ,
defined in bootargs. Just connect null modem cable and another PC ( tablet or 
smartphone with appropriate adapter ) and terminal emulator.
Error (and other) messages are usually hidden by `plymouth` for aesthetical reasons.

Perhaps this helps: If you hit ESC during shutdown, `plymouth` shows the graphical console. Does that show you useful messages?

Apart from that, there is little you can do if the machine actually crashes because it may not be able to write the log file - whether it is buffered, or `/var/log` is already remounted read-only, depending on when the crash occurs. You could have a look at these files by executing `ls -ltr /var/log` and looking whether there is a log file that matches your shutdown date (or newer).