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We study the discrete-time approximation for solutions of forward-backwardstochas- tic dierential equations (FBSDEs) with a jump. In this part, we studythe case of Lipschitz generators, and we refer to the second part of this work[15] for the quadratic case. Our method is based on a result given in thecompanion paper [14] which allows to link a FBSDE with a jump with a recursivesystem of Brownian FBSDEs. Then we use the classical results on discretizationof Brownian FBSDEs to approximate the recursive system of FBSDEs and werecombine these approximations to get a dis- cretization of the FBSDE with ajump. This approach allows to get a convergence rate similar to that of schemesfor Brownian FBSDEs.

A decomposition approach for the discrete-time approximation of FBSDEs with a jump I : the Lipschitz case