Package libapache2-mod-auth-mysql is not available
According to this thread the libapache2-mod-auth-mysql package is no longer maintained, and not needed:
I get the impression that many people have ended up here because they want to install a LAMP stack, since some instructions somewhere state that this package should be installed to get a LAMP stack. This is incorrect. This package is only required for Apache authentication against MySQL (as opposed to doing it at the web app end, which is far more common). It appears to me that there are cargo culted instructions floating around the Internet.
I just installed a LAMP stack without that package, and it works fine.
sudo apt-get install php5-mysql phpmyadmin
I also just installed the package without libapache2-mod-auth-mysql.
Seems to work just fine.
sudo apt-get install mysql-server php5-mysql phpmyadmin