The Laser Interferometer Space Antenna (LISA) is a future space-based gravitational wave observatory with launch planned in 2035. LISA will open a new window in the gravitational wave spectrum, observing sources in the millihertz band. Among the numerous sources LISA is expected to observe, some have the potential of emitting electromagnetic counterparts. Multi-messenger sources are of great scientific value, having the potential to address questions in astrophysics, cosmology and fundamental physics. From an observational point of view, joint detection of both gravitational and electromagnetic waves is a challenge. In particular, it requires early and precise sky-localization of target sources from gravitational observation. To address this problem, we develop and explore a model-agnostic sky-localization technique for LISA: coronagraphic time-delay interferometry (TDI). As a proof of concept, we first apply this technique to two typical LISA sources–Galactic binaries and massive black hole binaries–simulated without noise. We then increase the level of realism in the simulations, including instrumental noise and the motion of LISA spacecraft, to assess the robustness of the method. Finally, we investigate Bayesian parameter estimation with coronagraphic TDI, taking into account the time constraints imposed on low-latency searches with LISA.