  We present a new nearby young moving group (NYMG) kinematic membership
analysis code, LocAting Constituent mEmbers In Nearby Groups (LACEwING), a new
Catalog of Suspected Nearby Young Stars, a new list of bona fide members of
moving groups, and a kinematic traceback code. LACEwING is a convergence-style
algorithm with carefully vetted membership statistics based on a large
numerical simulation of the Solar Neighborhood. Given spatial and kinematic
information on stars, LACEwING calculates membership probabilities in 13 NYMGs
and three open clusters within 100 pc. In addition to describing the inputs,
methods, and products of the code, we provide comparisons of LACEwING to other
popular kinematic moving group membership identification codes. As a proof of
concept, we use LACEwING to reconsider the membership of 930 stellar systems in
the Solar Neighborhood (within 100 pc) that have reported measurable lithium
equivalent widths. We quantify the evidence in support of a population of young
stars not attached to any NYMGs, which is a possible sign of new
as-yet-undiscovered groups or of a field population of young stars.
