  We define the notions of $S_t^1\times S_s^1$-valued lightcone Gauss maps,
lightcone pedal surface and Lorentzian lightcone height function of Lorentzian
surface in semi-Euclidean 4-space and established the relationships between
singularities of these objects and geometric invariants of the surface as
applications of standard techniques of singularity theory for the Lorentzian
lightcone height function.
