LaCuSb2 is a superconductor with a transition temperature of about Tc = 0.9 K and is a potential platform where Dirac fermions can be experimentally observed. In this paper, we report systematic high-resolution studies of its electronic structure using the angle-resolved photoemission spectroscopy (ARPES) technique supported by the DFT calculation. The Fermi surface consists of four branches, of which the two inner ones are more 3-dimensional and the theoretical calculations reproduce well the experiment. We observe several linear dispersions forming Dirac-like structures. The nodal lines are present in the system along the M–A and X–R and Dirac crossings along the X–R are observed by ARPES. Finally, the nesting between external Fermi surface pockets, which corresponds to charge density wave (CDW) modulation vector is enhanced in LaCuSb2 as compared to LaAgSb2, while CDW appears in the latter system.