We report on single crystal growth, single crystal x-ray diffraction, physical properties and density functional theory (DFT) electronic structure as well as Fermi surface calculations for two ternary carbides, LuCoC2 and LuNiC2. Electrical resistivity measurements reveal for LuNiC2 a charge density wave (CDW) transition at TCDW 450 K and, for T > TCDW, a significant anisotropy of the electrical resistivity, which is lowest along the orthorhombic a-axis. The analysis of x-ray superstructure reflections suggest a commensurate CDW state with a Peierls-type distortion of the Ni atom periodicity along the orthorhombic a-axis. DFT calculations based on the CDW modulated monoclinic structure model of LuNiC2 as compared to results of the orthorhombic parent-type reveal the formation of a partial CDW gap at the Fermi level which reduces the electronic density of states from N (EF) = 1.03 states/eV f.u. without CDW to N (EF) = 0.46 states/eV f.u. in the CDW state. The corresponding bare DFT Sommerfeld value of the latter, γ CDW DFT = 0.90 mJ/mol K 2 , reaches reasonable agreement with the experimental value γ = 0.83(5) mJ/mol K 2 of LuNiC2. LuCoC2 displays a simple metallic behavior with neither CDW ordering nor superconductivity above 0.4 K. Its experimental Sommerfeld coefficient, γ = 5.9(1) mJ/mol K 2 , is in realistic correspondence with the calculated, bare Sommerfeld coefficient, γDFT = 3.82 mJ/mol K 2 , of orthorhombic LuCoC2.