In this article we introduce a notion of normalized angle for Lorentzian
pre-length spaces. This concept allows us to prove some equivalences to the
definition of timelike curvature bounds from below for Lorentzian pre-length
spaces. Specifically, we establish some comparison theorems known as the local
Lorentzian version of the Toponogov theorem and the Alexandrov convexity
property. Finally, as an application we obtain a first variation Formula for
non-negatively curved globally hyperbolic Lorentzian length spaces