Motivated by the novel insulating state of Sr_{2}IrO_{4} from strong spin-orbit coupling (SOC), we investigate, by means of angle resolved photoemission, the metal-insulator transition (MIT) mechanism in Sr_{2-x}La_{x}RhO_{4} whose mother compound is isovalent and isostructural but has smaller SOC strength compared to Sr_{2}IrO_{4}. Transport and angle resolved photoemission results from single crystalline Sr_{2-x}La_{x}RhO_{4} revealed that the MIT occurs coincidentally with a multi- to single-band transition (Lifshitz transition) at x=0.4. Starting from x=0.4, there is a gradual but anomalous enhancement in the band gap size with additional electron doping, suggesting that the insulating phase in Sr_{2-x}La_{x}RhO_{4} is a new type which has been rarely investigated. These results suggest that the insulating phase in Sr_{2-x}La_{x}RhO_{4} is likely induced by the moderate SOC strength and electron doping effect from the La. Our findings not only elucidate the MIT mechanism in Sr_{2-x}La_{x}RhO_{4}, but may also open new avenues for novel MIT research in moderate SOC regimes.