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A new causal boundary, which we will term the l-boundary, inspired by the geometry of the space of light rays and invariant by conformal diffeomorphisms for space-times of any dimension m >= 3, proposed by one of the authors [R. J. Low, The Space of Null Geodesics (and a New Causal Boundary), Lecture Notes in Physics 692 (Springer, 2006), pp. 35-50] is analyzed in detail for space-times of dimension 3. Under some natural assumptions, it is shown that the completed space-time becomes a smooth manifold with boundary and its relation with Geroch-Kronheimer-Penrose causal boundary is discussed. Anumber of examples illustrating the properties of this newcausal boundary as well as a discussion on the obtained results will be provided. Published by AIP Publishing.