We present the results of a Spitzer IRAC and MIPS 24 mu m study of extended Lyman-alpha clouds (or Lyman-alpha Blobs, LABs) within the SSA22 filamentary structure at z = 3.09. We detect 6/26 LABs in all IRAC filters, four of which are also detected at 24 mu m, and find good correspondence with the 850 mu m measurements of Geach et al. An analysis of the rest-frame ultraviolet, optical, near-and mid-infrared colors reveals that these six systems exhibit signs of nuclear activity (active galactic nucleus (AGN)) and/or extreme star formation. Notably, they have properties that bridge galaxies dominated by star formation (Lyman-break galaxies (LBGs)) and those with AGNs (LBGs classified as QSOs). The LAB systems not detected in all four IRAC bands, on the other hand, are, as a group, consistent with pure star-forming systems, similar to the majority of the LBGs within the filament. These results indicate that the galaxies within LABs do not comprise a homogeneous population, though they are also consistent with scenarios in which the gas halos are ionized through a common mechanism such as galaxy-scale winds driven by the galaxies within them, or gravitational heating of the collapsing cloud itself.