  The Laser Interferometer Space Antenna (LISA) will be a space-borne
gravitational wave (GW) detector to be launched in the next decade. Central to
LISA data analysis is time-delay interferometry (TDI), a numerical procedure
which drastically reduces otherwise overwhelming laser frequency noise. LISA
data analysis is usually performed on sets of TDI variables, e.g. Michelson
variables $(X, Y, Z)$ or quasiorthogonal variables $(A, E, T)$. We investigate
a less standard TDI variable denoted $\kappa$ which depends on time, or
frequency, and two parameters $(\beta, \lambda)$. This so-called coronagraphic
TDI variable has the singular property of canceling GW signal when $(\beta,
\lambda)$ tend to the sky position of the GW source. Thanks to this property,
coronagraphic TDI has the potential to be an efficient model-agnostic method
for sky localization of GW sources with LISA. Those characteristics make it
relevant for low-latency searches and a possible glitch veto. Although briefly
discussed in the literature, coronagraphic TDI has only been tested on
theoretical grounds. In this paper we validate the applicability of $\kappa$ to
sky localization of typical LISA sources, namely Galactic binaries (GBs) and
massive black hole binaries (MBHBs), when considering a simplified LISA
instrument. The goal of this paper is to pave the way for applications of
coronagraphic TDI to practical LISA data analysis problems.
