I've always seen it stand for Python, Perl or PHP-- with many shops specifically stating "P for PHP" or "P for Perl". Yahoo hasn't settled on PHP vs. mod_perl (as a replacement for a C based template system filo built) until early 2000s and (when I was there) still had many Perl based services in production.
When I interned at SBC/Yahoo DSL around 'mid 2000s, they used the LAMPerl stack quite extensively.
I think I remember around 2005 being surprised at hearing PHP stand in for the P, before that it had always been Perl. Though it probably had to do with the circles you ran in.
Maybe. We did LAMP before I heard the term, with a site in '98, but then it was definitely Perl. I've understood it as mainly Perl, and later PHP or Python as possibilities.