Aaaaah. So you didn't have iTunes to begin with... You said you had a Mac so I figured you also had iTunes.
Ok, iTunes doesn't have anything to do with Limewire other than the fact that LW's developers were kind enough to include a iTunes support function in LW.
As for the .m4a format, you can see it when you dld a song via LW under one of the columns that displays the extension of the file that you are about to dld or are already dlding (in the Search window). Generally, when you look for music in LW it will be in .mp3, with occasional .wma here and there as well as .ogg.
Now, fi you want to check what kind of format the files you already dlded are in, then simply find the file in the Finder and click it's name: you will be able to alter the name at that piont, but more importantly, you will be able to see the full name of the file, as well as it's extension (the very last letters after the .)
Since you dlded iTunes, if it works well (it's probably a cracked version) you can reencode the files from .m4a to .mp3 format by going to the preferences and changing the codec, as I said earlier. After that, if you wish to keep iTunes, then you can enable LW's iTunes support which will automatically import any songs you may dld later in one of iTunes' playlists, which will keep your files organized and close at hand.
iTunes is not necessary in order to use LW so it's a matter of personal choice.

__________________
iMac G4 OSX 10.3.9
RAM 256MB
LW 4.10.5 Basic
ADSL anything from 3 to 8Mbps/around 1024kbps

"Raise your can of Beer on high
And seal your fate forever
Our best years have passed us by
The Golden Age Of Leather"
-Blue Öyster Cult-