Nanite is a system for efficiently rendering masses of geometry (more so than using traditional methods)
Lumen is a technique to enable global illumination (rendering with multiple light bounces, traditional engines do 1 bounce + trickery) by first converting geometry to signed distance fields. Signed distance field techniques are very interesting, swapping triangles for analytic surface equations, they can be used to accelerate complex physics and lighting calculations. They've only recently started making their way into big commercial engines – starting with Media Molecule's Dreams game and now in UE5
Lumen deep dive: https://docs.unrealengine.com/5.0/en-US/RenderingFeatures/Lu...
Signed Distance Functions, Inigo Quilezles: https://iquilezles.org/www/articles/distfunctions/distfuncti...