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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 Lorentziansurface in semi-Euclidean 4-space and established the relationships betweensingularities of these objects and geometric invariants of the surface asapplications of standard techniques of singularity theory for the Lorentzianlightcone height function.

$S_t^1\times S_s^1$-valued lightcone Gauss map of a Lorentzian surface in semi-Euclidean 4-space