  We study the problem of phase transitions from 3D topological to normal
insulators without inversion symmetry. In contrast with the conclusions of some
previous work, we show that a Weyl semimetal always exists as an intermediate
phase regardless of any constriant from lattice symmetries, although the
interval of the critical region is sensitive to the choice of path in the
parameter space and can be very narrow. We demonstrate this behavior by
carrying out first-principles calculations on the noncentrosymmetric
topological insulators LaBiTe$_3$ and LuBiTe$_3$ and the trivial insulator
BiTeI. We find that a robust Weyl-semimetal phase exists in the solid solutions
LaBi$_{1-x}$Sb$_x$Te$_3$ and LuBi$_{1-x}$Sb$_x$Te$_3$ for
$x\!\approx\!38.5-41.9$\% and $x\!\approx\!40.5-45.1$\% respectively. A
low-energy effective model is also constructed to describe the critical
behavior in these two materials. In BiTeI, a Weyl semimetal also appears with
applied pressure, but only within a very small pressure range, which may
explain why it has not been experimentally observed.
