  The self-lensing of a massive black hole binary (MBHB), which occurs when the
two BHs are aligned close to the line of sight, is expected to produce
periodic, short-duration flares. Here we study the shapes of self-lensing
flares (SLFs) via general-relativistic ray tracing in a superimposed binary BH
metric, in which the emission is generated by geometrically thin accretion
flows around each component. The suite of models covers eccentric binary
orbits, black hole spins, unequal mass binaries, and different emission model
geometries. We explore the above parameter space, and report how the light
curves change as a function of, e.g., binary separation, inclination, and
eccentricity. We also compare our light curves to those in the microlensing
approximation, and show how strong deflections, as well as time-delay effects,
change the size and shape of the SLF. If gravitational waves (GWs) from the
inspiraling MBHB are observed by LISA, SLFs can help securely identify the
source and localizing it on the sky, and to constrain the graviton mass by
comparing the phasing of the SLFs and the GWs. Additionally, when these systems
are viewed edge-on the SLF shows a distinct dip that can be directly correlated
with the BH shadow size. This opens a new way to measure BH shadow sizes in
systems that are unresolvable by current VLBI facilities.
