  Without Lorentz symmetry, generic fixed points of the renormalization group
(RG) are labelled by their dynamical (or `Lifshitz') exponent $z$. Hence, a
rich variety of possible RG flows arises. The first example is already given by
the standard non-relativistic limit, which can be viewed as the flow from a
$z=1$ UV fixed point to a $z=2$ IR fixed point. In strongly coupled theories,
there are good arguments suggesting that Lorentz invariance can emerge
dynamically in the IR from a Lorentz violating UV. In this work, we perform a
generic study of fixed points and the possible RG flows among them in a minimal
bottom-up holographic model without Lorentz invariance, aiming to shed light on
the possible options and the related phenomenology. We find: i) A minor
generalization of previous models involving a massive vector field with allowed
self-couplings leads to a much more efficient emergence of Lorentz invariance
than in the previous attempts. Moreover, we find that generically the larger is
the UV dynamical exponent $z_{UV}$ the faster is the recovery of Lorentz
symmetry in the IR. ii) We construct explicitly a holographic model with a line
of fixed points, realizing different Lifshitz scaling along the line. iii) We
also confirm the monotonicity of a recently proposed a-function along all our
Lorentz violating RG flows.
