We observed RZ LMi, which is renowned for the extremely (~19d) short supercycle and is a member of a small, unusual class of cataclysmic variables called ER UMa-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, 60d for three consecutive superoutbursts. We consider that the object virtually experienced a transition to the novalike state (permanent superhumper). This observed behavior extremely well reproduced the prediction of the thermal-tidal instability model. 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 the orbital period of 0.05792d, which suggests a mass ratio of 0.105(5). This relatively large mass ratio is even above ordinary SU UMa-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 core evolved secondary which are evolving toward an AM CVn-type object.
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