A new but rare sample of spatially extended emission line nebulae, nicknamed Green Beans, was discovered at z~0.3 thanks to strong [OIII] emission, and subsequently shown to be local cousins of the Lyman-alpha (Lya) nebulae found at high redshift. Here we use follow-up APO/DIS spectroscopy to better understand how these low redshift Lya nebulae compare to other populations of strong emission line sources. Our spectroscopic data show that low-z Lya nebulae have AGN-like emission line ratios, relatively narrow line widths (FWHM<1000 km s^{-1}), and emission line kinematics resembling those of Type 2 AGN at the same redshift, confirming that they are powered by Type 2 AGN with typical ionizing continua. While low-z Lya nebulae are larger and less concentrated than compact, star-forming Green Pea galaxies, we find that they resemble typical Type 2 AGN in terms of r-band concentration and size. Based on this pilot study, low-z Lya nebulae appear to be a subset of Type 2 AGN with bluer optical continua and high [OIII] equivalent widths but with comparable sizes and similar [OIII] kinematics. These characteristics may simply reflect the fact that low-z Lya nebulae are drawn from the high luminosity end of the Type 2 AGN distribution, with higher nuclear activity driving higher [OIII] equivalent widths and more central star formation leading to bluer optical continua. Deeper spectroscopic follow-up of the full sample will shed further light on these issues and on the relationship between these low-z Lya nebulae and the Lya nebula population at high redshift.