Do WordPress Permalinks Refer to a Lookup Table in the Database?

No, for the most part.

WordPress stores its rewrite rules in the database. These are pattern-based rules for mapping URLs onto query parameters, and are determined by the permalink structure you've chosen (e.g. %post_name%) and any additional structures plugins have provided.

For single items, WordPress extracts either %post_id% or %post_name% (slug) from the URL and fetches that post from the posts table.

1. You have a set of url patterns and matches (wp generate a number of url patters to satisfy user agents).
2. once you request lets say domain.com/posts/2003/somestuff url, wp tring to find a pattern that match this url inside a rewrite_rules (array that stored in options table by option name rewrite_rules)
3. once it found... its parsed to query or better to say - matched_rule
4. matched rule basicly looks like dirty url (a url of wp site without turned on permalinks) , and matched_rule is a set of arguments that passed to WP_Query.
5. Once WP_Query get arguments and return some data (posts/pages/etc...) all of this data (wp_query and results) passed to view (template), index.php/single.php/etc.php
6. And here you got a page.

This is human explanation without (almost without) any tech details. Hope its undestandable for everyone who didn't work with rewrite_rules