X-ray continuum emission of active galactic nuclei (AGNs) may be reflected by circumnuclear dusty tori, producing prominent fluorescence iron lines at X-ray frequencies. Here, we discuss the broadband emission of three radio-loud AGNs belonging to the class of compact symmetric objects (CSOs), with detected narrow Fe Kα lines. CSOs have newly born radio jets, forming compact radio lobes with projected linear sizes of the order of a few to hundreds of parsecs. We model the radio-to-γ-ray spectra of compact lobes in J1407+2827, J1511+0518, and J2022+6137, which are among the nearest and the youngest CSOs known to date, and are characterized by an intrinsic X-ray absorbing column density of N > 10 cm. In addition to the archival data, we analyze the newly acquired Chandra X-ray Observatory and Submillimeter Array (SMA) observations, and also refine the γ-ray upper limits from Fermi Large Area Telescope monitoring. The new Chandra data exclude the presence of the extended X-ray emission components on scales larger than 1.''5. The SMA data unveil a correlation between the spectral index of the electron distribution in the lobes and N, which can explain the γ-ray quietness of heavily obscured CSOs. Based on our modeling, we argue that the inverse-Compton emission of compact radio lobes may account for the intrinsic X-ray continuum in all these sources. Furthermore, we propose that the observed iron lines may be produced by a reflection of the lobes' continuum from the surrounding cold dust.