Supporting faced search and other functionality requiring access to per document field-values is just an extension over the core IR functionality.

Tracking (document, field) values can be used for query by range or by geolocation primitives (that's what Lucene does, where it will index that data into a special tree-like structure, and for each query, it will build a custom 'iterator' and use it along with other iterators to match documents), and for static ranking of matched documents.

BTW, Lucene and Algolia are vastly different in terms of the underlying architecture.