Recent discoveries of recombining plasmas (RPs) in supernova remnants (SNRs) have dramatically changed our understanding of SNR evolution. To date, a dozen of RP SNRs have been identified in the Galaxy. Here we present Suzaku deep observations of four SNRs in the Large Magellanic Cloud (LMC), N49, N49B, N23, and DEM L71, for accurate determination of their plasma state. Our uniform analysis reveals that only N49 is in the recombining state among them, which is the first robust discovery of a RP from an extra-galactic SNR. Given that RPs have been identified only in core-collapse SNRs, our result strongly suggests a massive star origin of this SNR. On the other hand, no clear evidence for a RP is confirmed in N23, from which detection of recombination lines and continua was previously claimed. Comparing the physical properties of the RP SNRs identified so far, we find that all of them are categorized into the mixed-morphology class and interacting with surrounding molecular clouds. This might be a key to solve formation mechanisms of the RPs.