We use deep integral field spectroscopy data from the CALIFA survey to study the warm interstellar medium (WIM) of 32 nearby early-type galaxies (ETGs). We propose a tentative subdivision of our sample ETGs into two groups, according to their Ha equivalent width (EW) and Lyman continuum (LyC) photon escape fraction (PLF). Type i ETGs show nearly constant EWs and a PLF~0, suggesting that photoionization by post-AGB stars is the main driver of their faint extranuclear nebular emission. Type ii ETGs are characterized by very low, outwardly increasing EWs, and a PLF as large as ~0.9 in their centers. Such properties point to a low, and inwardly decreasing WIM density and/or volume filling factor. We argue that, because of extensive LyC photon leakage, emission-line luminosities and EWs are reduced in type ii ETG nuclei by at least one order of magnitude. Consequently, the line weakness of these ETGs is by itself no compelling evidence for their containing merely weak (sub-Eddington accreting) active galactic nuclei (AGN). In fact, LyC photon escape, which has heretofore not been considered, may constitute a key element in understanding why many ETGs with prominent signatures of AGN activity in radio continuum and/or X-ray wavelengths show only faint emission lines and weak signatures of AGN activity in their optical spectra. The LyC photon escape, in conjunction with dilution of nuclear EWs by line-of-sight integration through a triaxial stellar host, can systematically impede detection of AGN in gas-poor galaxy spheroids through optical emission-line spectroscopy. We further find that type i and ii ETGs differ little (~0.4 dex) in their mean BPT line ratios, which in both cases are characteristic of LINERs. This potentially hints at a degeneracy of the projected, luminosity-weighted BPT ratios for the specific 3D properties of the WIM in ETGs. (abridged)
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