How can I convert iPhone .m4a recordings to a more common and lossless format?

If the song is already in iTunes, it's easy to do it right within it. Go to the iTunes Preferences and choose "Import Settings" on the "General" page. You can set the desired output format here. Afterwards, select the songs you would like to convert and choose Advanced > Create XY Version, where XY is the file format you specified in the Import Settings. When iTunes has finished converting the files, you will have each track twice - you could use a smart playlist to filter the ones in the new format.

Bear in mind that converting from one lossy format to another lossy format will always result in a lower quality.

You can download Max (then File > Convert file).

Max can generate audio in over 20 compressed and uncompressed formats including MP3, Ogg Vorbis, FLAC, AAC, Apple Lossless, Monkey's Audio, WavPack, Speex, AIFF, and WAVE.

Max is integrated with MusicBrainz to permit automatic retrieval of compact disc information. For MP3, FLAC, Ogg FLAC, Ogg Vorbis, Monkey's Audio, WavPack, AAC and Apple Lossless files Max will write this metadata to the output.

QuickTime will export most sound files in the m4a container to many common formats, including mp3. There are many utilities where you can drag and drop, but free, capable, included with every mac is hard to beat.

Especially with Automator to automate the conversion using a folder action.

Also, iTunes will convert tracks for you. Simply change the import settings to be AIFF / WAV / Apple Lossless and right click and convert your songs (you can select several and they will all be converted sequentially.) Watch to clean up the duplicates in your library.