  Topological Lifshitz phase transition characterizes an abrupt change of the
topology of the Fermi surface through a continuous deformation of parameters.
Recently, Lifshitz transition has been predicted to separate two types of Weyl
points: type-I and type-II (or called structured Weyl points), which has
attracted considerable attention in various fields. Although recent
experimental investigation has seen a rapid progress on type-II Weyl points, it
still remains a significant challenge to observe their characteristic Lifshitz
transition. Here, we propose a scheme to realize both type-I and type-II Weyl
points in three-dimensional ultracold atomic gases by introducing an
experimentally feasible configuration based on current spin-orbit coupling
technology. In the resultant Hamiltonian, we find three degenerate points: two
Weyl points carrying a Chern number $-1$ and a four-fold degenerate point
carrying a Chern number $2$. Remarkably, by continuous tuning of a convenient
experimental knob, all these degenerate points can transition from type-I to
type-II, thereby providing an ideal platform to study different types of Weyl
points and directly probe their Lifshitz phase transition.
