Biomolecular condensates can be functional (e.g., as membrane-less organelles) or dysfunctional (e.g., as precursors to pathological protein aggregates). A major physical underpinning of biomolecular condensates is liquid liquid phase separation (LLPS) of proteins and nucleic acids. Here we investigate the effects of temperature and pressure on the LLPS of the eye-lens protein gamma-crystallin using UV/vis and IR absorption, fluorescence spectroscopy, and light microscopy to characterize the mesoscopic phase states. Quite unexpectedly, the LLPS of gamma-crystallin is much more sensitive to pressure than folded states of globular proteins. At low temperatures, the phase-separated droplets of gamma-crystallin dissolve into a homogeneous solution at as low as similar to 0.1 kbar whereas proteins typically unfold above similar to 3 kbar. This observation suggests, in general, that organisms thriving under high-pressure conditions in the deep sea, with pressure of up to 1 kbar, have to cope with this pressure sensitivity of biomolecular condensates to avoid detrimental impacts to their physiology. Interestingly, our experiments demonstrate that trimethylamine-N-oxide, an osmolyte upregulated in deep-sea fish, significantly enhances the stability of the condensed protein droplets, pointing to a previously unrecognized aspect of the adaptive advantage of increased concentrations of osmolytes in deep-sea organisms. As the birth place of life on earth could have been the deep sea, studies of pressure effects on LLPS as presented here are relevant to the possible formation of protocells under prebiotic conditions. A physical framework to conceptualize our observations and further ramifications of biomolecular LLPS at low temperatures and high hydrostatic pressures is discussed.