  A first-order-like resistivity hysteresis is induced by a subtle structural
transition under hydrostatic pressure in the topological nodal-line
superconductor PbTaSe$_2$. This structure transition is quickly suppressed to
zero at pressure $\sim$0.25 GPa. As a result, superconductivity shows a marked
suppression, accompanied with fundamental changes in the magnetoresistance and
Hall resistivity, suggesting a Lifshitz transition around $\sim$0.25 GPa. The
first principles calculations show that the spin-orbit interactions partially
gap out the Dirac nodal line around $K$ point in the Brillouin zone upon
applying a small pressure, whilst the Dirac states around $H$ point are
completely destroyed. The calculations further reveal a second structural phase
transition under a pressure as high as $\sim$30 GPa, through which a transition
from a topologically nontrivial phase to a trivial phase is uncovered, with a
superconducting dome emerging under this high-pressure phase.
