  The novel data analysis challenges posed by the Laser Interferometer Space
Antenna (LISA) arise from the overwhelmingly large number of astrophysical
sources in the measurement band and the density with which they are found in
the data. Robust detection and characterization of the numerous gravitational
wave sources in LISA data can not be done sequentially, but rather through a
simultaneous global fit of a data model containing the full suite of
astrophysical and instrumental features present in the data. While previous
analyses have focused on individual source types in isolation, here we present
the first demonstration of a LISA global fit analysis containing combined
astrophysical populations. The prototype pipeline uses a blocked Metropolis
Hastings algorithm to alternatingly fit to a population of ultra compact
galactic binaries, known ``verification binaries'' already identified by
electromagnetic observations, a population of massive black hole mergers, and
an instrument noise model. The Global LISA Analysis Software Suite (GLASS) is
assembled from independently developed samplers for the different model
components. The modular design enables flexibility to future development by
defining standard interfaces for adding new, or updating additional, components
to the global fit without being overly prescriptive for how those modules must
be internally designed. The GLASS pipeline is demonstrated on data simulated
for the LISA Data Challenge 2b. Results of the analysis and a road-map for
continued development are described in detail.

General Relativity and Quantum Cosmology;High Energy Astrophysical Phenomena;Instrumentation and Methods for Astrophysics