  One of the key astrophysical sources for the Laser Interferometer Space
Antenna (LISA) are the inspirals of stellar-origin compact objects into massive
black holes in the centres of galaxies. These extreme-mass-ratio inspirals
(EMRIs) have great potential for astrophysics, cosmology and fundamental
physics. In this paper we describe the likely numbers and properties of EMRI
events that LISA will observe. We present the first results computed for the
2.5 Gm interferometer that was the new baseline mission submitted in January
2017 in response to the ESA L3 mission call. In addition, we attempt to
quantify the astrophysical uncertainties in EMRI event rate estimates by
considering a range of different models for the astrophysical population. We
present both likely event rates and estimates for the precision with which the
parameters of the observed sources could be measured. We finish by discussing
the implications of these results for science using EMRIs.
