What is the significance of the 'P' in LAMP? Why is it PHP, Perl, or Python?
I think you're trying to read too much into what it means.  The acronym became popular because they were often used together and it was easy to pronounce.  It doesn't have any meaning or implication beyond the literal one.  There's also WAMP (Windows), LAPP (PostgreSql) and whatever else you want to make up.
I'm a Java web developer that knows a bit of Python (but haven't done any Python web development), and I am curious what exactly is meant by a LAMP stack.
I understand this to be Linux-Apache-MySQL-(PHP, Perl, or Python), but I don't understand what unites these three languages other than the letter P.
Is a LAMP stack fundamentally different if Ruby was used? Using Ruby would typically mean using Rails, but Python web apps usually use Django or Pylons. Or does LAMP signify that no framework is used? Is Java web development essentially different because of Tomcat in place of Apache?