For example, the LuxRender addon texture data is arranged such that the properties for each Lux texture type are arranged into nested IDPropertyGroups (IDPG), and the 'top-level' group describes which Lux texture to use:

top-level IDPG: bpy.data.textures['IOR_G-07'].luxrender_texture

If bpy.data.textures['IOR_G-07'].luxrender_texture.type == 'cauchy', then the addon will look for additional properties in the corresponding sub-IDPG:

bpy.data.textures['IOR_G-07'].luxrender_texture.luxrender_tex_cauchy

This particular sub-IDPG contains a couple of FloatProperties, one of which is:

bpy.data.textures['IOR_G-07'].luxrender_texture.luxrender_tex_cauchy.a

When I try to add a keyframe on that property, blender raises the following error:

Insert Key: Could not insert keyframe, as RNA Path is invalid for the given ID (ID = TEIOR_G-07, Path = a)

It should also be noted that although keyframe creation also seems to succeed for properties such as bpy.data.textures['IOR_G-07'].luxrender_texture.type, that the values do not appear in the Graph editor and do not change upon frame-change.
This is in contrast to the native property bpy.data.textures['IOR_G-07'].type, which is keyframeable, shows in the Graph editor and does change upon frame-change.

All in all, this problem means that none of the custom LuxRender properties can currently be animated.