The hack-job appeared to work, but whether it functions correctly or not is another thing entirely
SQLite3 module version 0.7-dev
SQLite Library 3.6.18
Installed a CMS that uses SQLite as a basic test and it seems to work okay.
Obviously this kinda thing should only be used with learning/development in mind - PHP 5.3 itself is bundled with SQLite versions lower than the latest 5.2 so it's likely unwise to send something running a knock-up build out into production.
I'll PM you the shell info so you can have a play around with it and let us know if the build really was successful or not.
You have PM's switched off here so I tried the email form at your site.
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How To Install PHP.INI / ionCube on DreamHost