A Lorentzian para-Sasakian (LP-Sasakian) structure is a particular case of a Lorentzian paracontact structure, introduced by the first author in [Bull. Yamagata Univ., Nat. Sci. 12, No.2, 151-156 (1989)]. By analogy with the Sasakian case studied by S. Kato
and M. Nagao
[Kodai Math. J. 18, 87-95 (1966)], in the present paper, the notion of infinitesimal CL-transformation in an LP-Sasakian manifold is defined and a homothetic conformal Killing vector field is obtained. A CL-relation between a symmetric affine connection and the Lorentzian metric connection is studied and the curvature tensor of the Lorentzian metric of a CL-flat LP-Sasakian manifold is obtained.