The model of limited enantioselectivity (LES) in closed systems, and under experimental conditions able to achieve chemical equilibrium, can give rise to neither spontaneous mirror symmetry breaking (SMSB) nor kinetic chiral amplifications. However, it has been recently shown that it is able to lead to SMSB, as a stationary final state, in thermodynamic scenarios involving nonuniform temperature distributions and for compartmentalized separation between the two autocatalytic reactions. Herein, it is demonstrated how SMSB may occur in LES in a cyclic network with uniform temperature distribution if the reverse reaction of the nonenantioselective autocatalysis, which gives limited inhibition on the racemic mixture, is driven by an external reagent, that is, in conditions that keep the system out of chemical equilibrium. The exact stability analysis of the racemic and chiral final outcomes and the study of the reaction parameters leading to SMSB are resolved analytically. Numerical simulations, using chemical kinetics equations, show that SMSB may occur for chemically reasonable parameters. Numerical simulations on SMSB are also presented for speculative, but reasonable, scenarios implying reactions common in amino acid chemistry.