We describe the enantiomeric and enantiotopic analysis of the NMR spectra of compounds derived from the functionalized cone-shaped core, cyclotriveratrylenes (CTV), dissolved in weakly oriented lyotropic chiral liquid crystals (CLCs) based on organic solutions of poly-gamma-benzyl-L-glutamate. The CTV core lacks prostereogenic as well as stereogenic tetrahedral centers. However, depending on the pattern of substitution, chiral and achiral compounds with different symmetries can be obtained. Thus, symmetrically nonasubstituted CTVs (C-3 symmetry) are optically active and exhibit enantiomeric isomers, while symmetrically hexasubstituted (C-3v symmetry) derivatives are prochiral and possess enantiotopic elements. In the first part we Use H-2 and C-13 NMR to study two nonasubstituted (-OH or -OCH3) CTVs, where the ring methylenes are fully deuterated, and show for the first time that the observation of enantiomeric discrimination of chiral molecules with a 3-fold symmetry axis is possible in a CLC. It is argued that this discrimination reflects different orientational ordering of the M and P isomers, rather than specific chiral short-range solvent-solute interactions that may affect differently the magnetic parameters of the enantiomers or even their geometry. In the second part we present similar measurements on hexasubstituted CTV with flexible side groups (-OC(O)CH3 and the, partially deuterated bidentate, -OCH2CH2O-), having on the average C-3v, symmetry. No spectral discrimination of enantiotopic sites was detected for the -OC(O)CH3 derivative. This is consistent with a recent theoretical work (J Chem. Phys. 1999, 111, 6890) that indicates that in C-3v molecules no chiral discrimination between enantiotopic elements, based on ordering, is possible. In contrast, a clear splitting was observed in the H-2 spectra of the enantiotopic deuterons of the side groups in the tri(dioxyethylene)-CTV. It is argued that this discrimination reflects different ordering characteristics of the various, rapidly (on the NMR time scale) interconverting conformers of this compound. Assuming two twisted structures for each of the dioxyethylene side groups, four different conformers are expected, comprising two sets of enantiomeric pairs with, respectively, C-3 and C-1 symmetries. Differential ordering and/or tractional population imbalance of these enantiomeric pairs leads to the observed spectral discrimination of sites in the side chains that on average form enantiotopic pairs.