  The Laser Interferometer Space Antenna (LISA) is scheduled to launch in the
mid 2030s, and is expected to observe gravitational-wave candidates from
massive black-hole binary mergers, extreme mass-ratio inspirals, and more.
Accurately inferring the source properties from the observed gravitational-wave
signals is crucial to maximise the scientific return of the LISA mission.
BILBY, the user-friendly Bayesian inference library, is regularly used for
performing gravitational-wave inference on data from existing ground-based
gravitational-wave detectors. Given that Bayesian inference with LISA includes
additional subtitles and complexities beyond it's ground-based counterpart, in
this work we modify BILBY to perform parameter estimation with LISA. We show
that full nested sampling can be performed to accurately infer the properties
of LISA sources from transient gravitational-wave signals in a) zero-noise and
b) idealized instrumental noise. By focusing on massive black-hole binary
mergers, we demonstrate that higher order multipole waveform models can be used
to analyse a year's worth of simulated LISA data, and discuss the computational
cost and performance of full nested sampling compared with techniques for
optimising likelihood calculations, such as the heterodyned likelihood.
