  Several integrable semi-discretizations are known in the literature for the
massive Thirring system in characteristic coordinates. We present for the first
time an integrable semi-discretization of the massive Thirring system in
laboratory coordinates. Our approach relies on the relation between the
continuous massive Thirring system and the Ablowitz-Ladik lattice. The Backlund
transformation for solutions to the Ablowitz-Ladik lattice and the time
evolution of the massive Thirring system in laboratory coordinates are combined
together in the derivation of the Lax system for the integrable
semi-discretization of the massive Thirring system.
