  The quantum limit (QL) of an electron liquid, realised at strong magnetic
fields, has long been proposed to host a wealth of strongly correlated states
of matter. Electronic states in the QL are, for example, quasi-one dimensional
(1D), which implies perfectly nested Fermi surfaces prone to instabilities.
Whereas the QL typically requires unreachably strong magnetic fields, the
topological semimetal ZrTe$_5$ has been shown to reach the QL at fields of only
a few Tesla. Here, we characterize the QL of ZrTe$_5$ at fields up to 64 T by a
combination of electrical-transport and ultrasound measurements. We find that
the Zeeman effect in ZrTe$_5$ enables an efficient tuning of the 1D Landau band
structure with magnetic field. This results in a Lifshitz transition to a 1D
Weyl regime in which perfect charge neutrality can be achieved. Since no
instability-driven phase transitions destabilise the 1D electron liquid for the
investigated field strengths and temperatures, our analysis establishes
ZrTe$_5$ as a thoroughly understood platform for potentially inducing more
exotic interaction-driven phases at lower temperatures.
