Despite recent progress in understanding Lyman-alpha (Lya) emitters (LAEs), relatively little is known regarding their typical black hole activity across cosmic time. Here, we study the X-ray and radio properties of ~4000 LAEs at 2.23) and find an average luminosity of 10^{44.07+-0.01} erg/s and an average black hole accretion rate (BHAR) of 0.42+-0.01 Msun/yr, consistent with moderate to high accreting AGN. We detect 120 sources in deep radio data, implying a LAE radio AGN fraction of 3.2+-0.3%. Approximately half of the LAEs detected in the radio are also detected in the X-rays, resulting in a total AGN fraction of 8.6+-0.4% for >L* LAEs. The total AGN fraction rises with Lya luminosity and declines with increasing redshift. For AGN, we find that Lya luminosities correlate with the BHARs, suggesting that Lya luminosity becomes an accretion rate indicator. Most LAEs (93.1+-0.6%) at 2
