The entire business? No, that's impossible. Every business is going to need at least some kind of accounting system (even if it's just a simple spreadsheet), and LAMP doesn't cover that at all.
Well hardburn, I guess that this depends on what your definition of "cover" means... SQL Ledger is written in Perl, runs under Apache (mod_perl) and can use PostgreSQL. (more here and here)
Still, I think you're right. There is much more to a business than the software architecture and there are certain tasks that are not that well covered in the OS world, so a ++ for you :)
-lem, but some call me fokat