Plasmonic lenses, even of simple design, may have intricate spectral behavior. The spectral response of a plasmonic lens to a local, broadband excitation has rarely been studied despite its central importance in future applications. Here we use the unique combination of scanning tunneling microscopy (STM) and angle-resolved optical spectroscopy to probe the spectral response of a plasmonic lens. Such a lens consists of a series of concentric circular slits etched in a thick gold film. Spectrally broad, circular surface plasmon polariton (SPP) waves are electrically launched from the STM tip at the plasmonic lens center, and these waves scatter at the slits into a narrow, out-of-plane, light beam. We show that the angular distribution of the emitted light results from the interplay of the size of the plasmonic lens and the spectral width of the SPP nanosource. We then propose simple design rules for optimized light beaming with the smallest possible footprint. The spectral distribution of the emitted light depends not only on the SPP nanosource, but on the local density of electromagnetic states (EM-LDOS) at the nanosource position, which in turn depends on the cavity modes of the plasmonic microstructure. The key parameters for tailoring the spectral response of the plasmonic lens are the period of the slits forming the lens, the number of slits, and the lens inner diameter.