There will be no problem.
You can mention a different path during compile. Just go through it's Install instructions on how to pass new path parameter to make/make install process.
This way both the Sqlite original and your new version can co-exist.
Running: Pay attention to run the new Sqlite from it's new location, specify absolute path to run it.
I hope you know how to write init and shutdown script to start & stop your new Sqlite install, as these will be different from what you already have in your /etc/init.d