For a discontinuous piecewise linear Li\'{e}nard system $\dot{x} = F(x)-y$, $\dot{y} = x$, where $F(x)$ is an $n$ piecewise linear function, the question of how many limit cycles it  can possess has been a classical and open problem in the theory of differential equations and dynamical systems. Up to now, this problem remains unresolved in general. This paper aims to provide an answer for the case $n=1$ of this open problem.  We prove that the maximum number of limit cycles for such a system with one discontinuity is $2$.  To this end, we start with the global phase portraits and bifurcation diagrams  of the discontinuous piecewise linear Li\'enard system for the case $n=1$. The system exhibits a wealth of interesting and rich dynamics, including the coexistence of crossing and sliding  cycles, grazing limit cycle bifurcations, and double limit cycle bifurcations, which may have potential interdisciplinary applications.