Probably no theoretical advantage in converting Lossless to AIFF, as the source material done first in AIFF would be a larger file (more "information", audible or not).
If the missing data made a difference I could hear (an improvement), I'd consider re-ripping the collection. It certainly wouldn't be the first time!
As Herman stated - there is no missing information. Think of it as compacing something in a zip file and then unzipping it. You could compare the unzipped file to the original bit for bit and not find a difference.
Anyway, if you go over to Computerasylum you will find many comments from people that did find a difference and pretty much everyone is attributing it to the real time unzipping as the data send do your DAC is in PCM format. For WAV/AIFF there is no conversion at all, so no additional processes when playing, thus a possible advantage.
Nevertheless for your stored files you can simply convert the files back from Lossless to AIFF and it should be identical to an original AIFF file if you compare bit for bit.