We observed RZ LMI, which is renowned for its extremely short (∼19 d) supercycle and is a member of a small, unusual class of cataclysmic variables called ERUMa-Type dwarf novae, in 2013 and 2016. In 2016, the supercycles of this object substantially lengthened in comparison to the previous measurements to 35, 32, and 60 d for three consecutive superoutbursts.We consider that the object virtually experienced a transition to the novalike state (permanent superhumper). This observed behavior reproduced the prediction of the thermal-Tidal instability model extremely well. We detected a precursor in the 2016 superoutburst and detected growing (stage A) superhumps with a mean period of 0.0602(1) d in 2016 and in 2013. Combined with the period of superhumps immediately after the superoutburst, the mass ratio is not as small as in WZ Sge-Type dwarf novae, having orbital periods similar to RZ LMI. By using least absolute shrinkage and selection operator (Lasso) two-dimensional power spectra, we detected possible negative superhumps with a period of 0.05710(1) d. We estimated an orbital period of 0.05792 d, which suggests a mass ratio of 0.105(5). This relatively large mass ratio is even above that of ordinary SUUMa-Type dwarf novae, and it is also possible that the exceptionally high mass-Transfer rate in RZ LMI may be a result of a stripped secondary with an evolved core in a system evolving toward an AM CVn-Type object.