This paper presents algorithmic and empirical contributions demonstrating that the convergence characteristics of a co-evolutionary approach to tackle Multi-Objective Games (MOGs) with postponed preference articulation can often be hampered due to the possible emergence of the so-called Red Queen effect. Accordingly, it is hypothesized that the convergence characteristics can be significantly improved through the incorporation of memetics (local solution refinements as a form of lifelong learning), as a promising means of mitigating (or at least suppressing) the Red Queen phenomenon by providing a guiding hand to the purely genetic mechanisms of co-evolution. Our practical motivation is to address MOGs of a time-sensitive nature that are characterized by computationally expensive evaluations, wherein there is a natural need to reduce the total number of true function evaluations consumed in achieving good quality solutions. To this end, we propose novel enhancements to co-evolutionary approaches for tackling MOGs, such that memetic local refinements can be efficiently applied on evolved candidate strategies by searching on computationally cheap surrogate payoff landscapes (that preserve postponed preference conditions). The efficacy of the proposal is demonstrated on a suite of test MOGs that have been designed.