Based off of https://github.com/Homebrew/linuxbrew/pull/330.

Currently building python on linux only looks for sqlite include paths in a hardcoded set of system paths, but if the user specifies -I/-L options during compilation, python setup.py looks there for sqlite3 as well, but only on OS X. This is problem for people who want to build python against a local version of sqlite3, and it is also inconsistent with the OS X behavior. Also the comments say that it should work on any unix-y OS!

This is essentially a duplicate of Issue3467 and various other similar issues.  While it may not be easy to justify the special case in setup.py for OS X (the reason was primarily for OS X installer builds), it would be even harder to justify adding another special case just for "Linux" systems.  Why not all platforms and libs?  The standard reply (in Issue3467 and elsewhere) to these kinds of requests has been to use one of the Modules/Setup files (like Setup.local) to customize extension module builds or to come up with a more general solution for the top-level setup.py third-party library configuration, rather than more special cases for each lib.

My apologies, I replied a bit too hastily, thinking incorrectly that your suggested change was just for sqlite3.  While the comments above still apply, there is already an open request for the more general feature (and more) under Issue21571.  So I suggest further discussion be moved there.