A bare quartz fiber with single refractive index is implanted into a polydimethylsiloxane (PDMS) microfluidic channel. The lasing gain medium consists of fluorescence resonance energy transfer (FRET) donor-acceptor dye pair Rhodamine B (RhB)-LDS821 mixture solution, which has a lower refractive index than that of the optical fiber and flows in the PDMS microfluidic channel. The circular cross section of the optical fiber forms a ring resonator and hosts high-quality (Q) whispering gallery modes (WGMs). Pumping along the optical fiber axis, the FRET characteristic parameters, i.e., the FRET efficiency \eta and the Förster distance R₀ of donor-acceptor dye pair, are firstly studied by using a continuous wave laser as a pump light source with a wavelength of 532 nm. The excited states are thencreated in the donor (RhB) by using a pulse laser with a wavelength of 532 nm and whose energy is transferred into the adjacent acceptor (LDS821) through the non-radiative FRET mechanism. Finaly, the emission of LDS821 iscoupled into the WGM of the ring resonator to lase. Due to the high energy transfer efficiency and high Q-factor, the acceptor shows a lasing threshold as low as 1.26 \textμ\rm J/mm².