You would have to define a custom projected coordinate system in ArcGIS, but it's certainly do-able. Lambert azimuthal equal area has always supported non-polar cases in ArcGIS for Desktop, and did in Workstation too.
Anyway, here's the well-known text string for the definition:
PROJCS["raster_laz",GEOGCS["GCS_Sphere_ARC_INFO",DATUM["D_Sphere_ARC_INFO",SPHEROID["Sphere_ARC_INFO",6370997.0,0.0]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],PROJECTION["Lambert_Azimuthal_Equal_Area"],PARAMETER["False_Easting",0.0],PARAMETER["False_Northing",0.0],PARAMETER["Central_Meridian",-100.0],PARAMETER["Latitude_Of_Origin",45.0],UNIT["Meter",1.0]]
Copy it as a single line to a text file, change the text file's extension to .prj, then you can import it through the raster's property page in ArcCatalog or the Define Projection tool.
Your next question may be on what geographic/datum transformation should be used to convert to NAD83 or WGS84-based coordinate system (or to overlay it with that type of data). There's no predefined transformations between a sphere-based GCS and a geodetic GCS (AKA one based on a true geodetic datum). Try just adding the raster with your other data, ignore any transformation warnings. Does it appear to overlay? Then you're good to go. If it appears to be offset north-south, try adding a custom geographic transformation (there's a tool) between its GCS and NAD83 or WGS84 whatever you're using. Set the method to Geocentric Translation and leave the parameter values set to zeroes.
Melita