An analysis is given of the capability of the LHC to detect narrow resonances using high luminosities and techniques for discriminating among models are discussed. The analysis is carried out with focus on the U(1)_X Abelian (Higgless) Stueckelberg extension of the Standard Model (StSM) gauge group which naturally leads to a very narrow Z' resonance. Comparison is made to another class of models, i.e., models based on the warped geometry which also lead to a narrow resonance via a massive graviton (G). Methods of distinguishing the StSM Z' from the massive graviton at the LHC are analyzed using the dilepton final state in the Drell-Yan process pp→Z'→l⁺l⁻ and pp→G→l⁺l⁻. It is shown that the signature spaces in the σ.Br(l⁺l⁻)-resonance mass plane for the Z prime and for the massive graviton are distinct. The angular distributions in the dilepton C-M system are also analyzed and it is shown that these distributions lie high above the background and are distinguishable from each other. A remarkable result that emerges from the analysis is the observation that the StSM model with Z' widths even in the MeV and sub-MeV range for Z' masses extending in the TeV region can produce detectable cross section signals in the dilepton channel in the Drell-Yan process with luminosities accessible at the LHC. While the result is derived within the specific StSM class of models, the capability of the LHC to probe models with narrow resonances in this range may hold more generally.