Abstract: The theory and automation of the exhaustive study of
links (including knots) in $S^3$ is understood. Extending these
methods to completely enumerate links in specified ambient spaces other than $S^3$ is less well understood. For any fixed lens space $L(p,q)$, we describe a method for producing all links with a prescribed complexity in the ambient $L(p,q)$. We demonstrate progress in software to automate the enumeration and feature extraction of lens space link complements and their fillings.