We consider the plane wave scattering and absorption characteristics of layered cylindrical Luneburg lens equipped with conformal strip of graphene, in the H-polarization case. The angular width of the strip is arbitrary and its surface impedance is characterized with aid of the quantum-physics Kubo formalism. We use mathematically accurate full-wave technique, which is based on the inversion of the problem static part. This means analytical regularization and guarantees convergence of the resulting numerical algorithm. We compute the backward scattering and absorption cross-sections of microsize configuration as a function of the frequency in wide range from zero to 6 THz. This analysis shows that the graphene strip, placed into the focal area of Luneburg lens, turns the latter into efficient absorber. Moreover, this broadband absorption is additionally enhanced at the resonance frequencies on the moderate-Q plasmon modes of graphene strip. © 2023 European Microwave Association (EuMA).