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The main result of this paper is that the Weyl anomaly of a $z=2$(1+1)-dimensional Lifshitz effective action can be derived from a(2+1)-dimensional non-relativistic Schr$\mathrm{\ddot{o}}$dinger-invariantChern-Simons (NRSCS) action which was shown to be equivalent to a specificWeyl-invariant non-projectable Horava-Lifshitz action of gravity. On a manifoldwith a boundary, we will show that the (1+1)-dimensional Lifshitz Weyl anomalycan be derived from a specific term, the torsional CS (tCS) term, in the NRSCSaction built from the gauge fields of the Weyl and special conformal symmetrygenerators of the centrally-extended Schr$\mathrm{\ddot{o}}$dinger algebra. Wealso focus on the $z=1$ Lifshitz Weyl anomaly and attempt to elicit itsgeometric and physical nature, in particular its relationship with the Lorentzanomaly of a (1+1)-dimensional CFT effective actions. We show that it isdirectly related to the curvature scalar of the dual Lorentz connection, theintegral of which is known to be a topological invariant. We also point outthat making the anomalous Lifshitz quantum effective action Weyl-invariantamounts to obtaining the equation of motion for a stationary chiral boson whichhappens to be the spatial-component of the acceleration vector. By puttingboundary conditions on the spatial slices, the time dependence of the lapsefunction in the Arnowitt, Deser and Misner (ADM) decomposition is eliminatedand the result is a Rindler metric. We finally discuss several issues relatedto the (1+1)-dimensional Lifshitz Weyl anomaly regarding edge physics offractional quantum Hall states and anomaly cancellation by anomaly inflow.

A (1+1)-dimensional Lifshitz Weyl Anomaly From a Schr$\mathrm{\ddot{o}}$dinger-invariant Non-relativistic Chern-Simons Action