Several pieces of astrophysical evidence, from galactic to cosmological scales,
indicate that most of the mass in the universe is composed of an invisible and
essentially collisionless substance known as dark matter. A leading particle
candidate that could provide the role of dark matter is the Weakly Interacting
Massive Particle (WIMP), which can be searched for directly on Earth via its
scattering off atomic nuclei. The LUX-ZEPLIN (LZ) experiment, currently under
construction, employs a multi-tonne dual-phase xenon time projection chamber to
search for WIMPs in the low background environment of the Davis Campus at the
Sanford Underground Research Facility (South Dakota, USA). LZ will probe WIMP
interactions with unprecedented sensitivity, starting to explore regions of the
WIMP parameter space where new backgrounds are expected to arise from the
elastic scattering of neutrinos off xenon nuclei.

In this work the theoretical and computational framework underlying the
calculation of the sensitivity of the LZ experiment to WIMP-nucleus scattering
interactions is presented. After its planned 1000 live days of exposure, LZ
will be able to achieve a $3\sigma$ discovery for spin independent cross
sections above 3.0e-48 cm^2 at 40 GeV/c^2 WIMP mass or exclude at
90\%~CL a cross section of 1.3e-48 cm^2 in the absence of signal. The
sensitivity of LZ to spin-dependent WIMP-neutron and WIMP-proton interactions is
also presented. All the sensitivity projections are calculated using the
LZStats software package, which is discussed in detail in this thesis.
In addition, this work classifies key systematic uncertainties by their impact
on the WIMP sensitivity and motivates the inclusion of the highest-ranked into
the analysis likelihood function. The effect of some of these systematics on the
reconstruction of the WIMP cross section is also studied and it is found to be
sub-dominant.