  We discuss the rationality of Lorentzian lattice conformal field theory
(LLCFT) recently constructed in arXiv:2312.16296 and obtain equivalent
characterizations of rationality generalising Wendland's rational Narain CFT
characterization. We then describe the construction of a modular tensor
category (MTC) associated to rational LLCFTs. We explicitly construct the
modular data and braiding and fusing matrices for the MTC. As a concrete
example, we show that the LLCFT based on a certain even, self-dual Lorentzian
lattice of signature $(m,n)$ with $m$ even realises the $D(m\bmod 8)$ level 1
Kac-Moody MTC.
