You’ve got to rewrite mysql_query() and some others in order to use it with SQLite Integration.
PDO for WordPress と Google Sitemaps Generator for WordPress(2010-05-23, written only in Japanese) reports workaround for PDO for SQLite plugin. But this patch is rejected for the newest version of Google XML Sitemap. I changed a little and newly created a patch file for SQLite Integration.->google-sitemap-generator_3.2.9.patch
Google (XML) Sitemaps Generator for WordPress Beta version (4.0b11 is the latest) works without patch file. And it doesn’t need static files and supports multisite installation and multilanguage. See the ChangeLog. I recommend this beta version.