Laser spectroscopy stands out as a powerful tool to investigate atomic and nuclear properties and also test fundamental theories by precisely measuring the energy levels in highly charged ions. In this work, the fine-structure splitting 1s²2s ²S_1/2 − 1s²2p ²P_1/2 transition in lithium-like ¹⁶O⁵⁺ has been investigated in a laser spectroscopy experiment at the heavy-ion storage ring CSRe. The excitation resonance of the tunable narrowband UV laser and the ions was observed using a Schottky resonator with very high sensitivity. The experimental uncertainties including the ion beam velocity determination, the space charge effects, laser wavelength calibration, and angular misalignment between the laser and ion beam were analyzed, and the ²S_1/2 −²P_1/2 transition wavelength was determined to be λ₀= 103.45(38) nm. The primary source of experimental uncertainty arises from the inaccurate measurement of the high voltage applied on the electron cooler and therewith the ion beam velocity at the CSRe. In order to solve this problem, a high-precision divider to precisely measure the high-voltage of the electron cooler is under construction, which is expected to improve the present experimental accuracy by three orders of magnitude. In addition, an XUV optical detector equipped with an off-axis parabolic mirror has been developed and installed at the CSRe for the investigation of slow dipole-forbidden transitions in highly charged ions, such as hyperfine splitting and M1 transitions. The experimental studies presented here pave the way for future laser spectroscopy experiments at the CSRe as well as at the future larger-scale scientific facility HIAF in China.