Spectroastrometry, which measures wavelength-dependent shifts in the center of light, is well-suited for studying objects whose morphology changes with wavelength at very high angular resolutions. Photonic lantern (PL)-fed spectrometers have the potential to enable the measurement of spectroastrometric signals because the relative intensities between the PL output SMFs contain spatial information on the input scene. To use PL output spectra for spectroastrometric measurements, it is important to understand the wavelength-dependent behaviors of PL outputs and develop methods to calibrate the effects of time-varying wavefront errors in ground-based observations. We present experimental characterizations of the three-port PL on the SCExAO testbed at the Subaru Telescope. We develop spectral response models of the PL and verify the behaviors with lab experiments. We find the sinusoidal behavior of astrometric sensitivity of the three-port PL as a function of wavelength, as expected from numerical simulations. Furthermore, we compare experimental and numerically simulated coupling maps and discuss their potential use for offsetting pointing errors. We then present a method of building PL spectral response models (solving for the transfer matrices as a function of wavelength) using coupling maps, which can be used for further calibration strategies.