Can positron annihilation lifetime spectroscopy (PALS) be employed to discriminate different types of soft tissues? This work reports our experimental measurements of the three components of positron annihilation lifetime spectra for three types of bovine, non-fixated soft tissues: adipose, hepatic, and muscle. These three components of PALS spectra correspond to contributions from annihilation lifetimes of para-positronium (p-Ps), positron, and ortho-positronium (o-Ps). We also report a benchmark comparison between PALS and X-ray phase-contrast imaging, which is the current state-of-the-art for soft tissue imaging and analysis. Our measurements showed that the joint probability of annihilation from p-Ps and positron in the soft tissues increases with electron density of the tissue and hence correlates well with the mean voxel values measured by X-ray phase-contrast computed tomography. Notably, the o-Ps lifetime in adipose tissue (2.53±0.01 ns) was approximately 25% longer than in hepatic (2.03±0.02 ns) and muscle tissues (2.00±0.01 ns). The significance here is that the o-Ps lifetime is a viable non-invasive probe for analyzing and discriminating the different soft tissues with a strong sensitivity to the lipid content of the tissue.