  We present the LyA emission line luminosity function (LF) of the Active
Galactic Nuclei (AGN) in the first release of the Hobby-Eberly Telescope Dark
Energy Experiment Survey (HETDEX) AGN catalog (Liu et al. 2022, Paper I). The
AGN are selected either by emission-line pairs characteristic of AGN or by
single broad emission line, free of any photometric pre-selections
(magnitude/color/morphology). The sample consists of 2,346 AGN spanning
1.88<z<3.53, covering an effective area of 30.61 deg^2. Approximately 2.6 of
the HETDEX AGN are not detected at $>5\sigma$ confidence at r~26 in the deepest
$r$-band images we have searched. The LyA line luminosity ranges from ~10^42.3
to ~10^45.9 erg s^-1. Our LyA LF shows a turnover luminosity with opposite
slopes on the bright end and the faint end: The space density is highest at
L_LyA^*=10^43.4 erg s^-1.
  We explore the evolution of the AGN LF over a broader redshift range
(0.8<z<3); constructing the rest-frame ultraviolet (UV) LF with the 1450 AA
monochromatic luminosity of the power-law component of the continuum ($\rm
M_{1450}$) from M_1450~-18 to ~-27.5. We divide the sample into three redshift
bins (z~1.5, 2.1, and 2.6). In all three redshift bins, our UV LFs indicate
that the space density of AGN is highest at the turnover luminosity M_1450^*
with opposite slopes on the bright end and the faint end. The M_1450 LFs in the
three redshift bins can be well-fit with a
luminosity-evolution-density-evolution (LEDE) model: the turnover luminosity
(M_1450^*) increases and the turnover density (Phi^*) decreases with increasing
redshift.
