Found this cool method to mod the music for the League of Legends login and champion select screens. As taken from the League of Legends forums, here are the instructions:
So to change the music of log-in screen and champ select all you have to do is follow these simple steps:
1. Download the song that you want to play in log in/champ select screen in MP3 format.
2. If you want that music to play in log-in screen then rename the mp3 file to: LoL_MUSIC_PVP_Login
If you want that music to play in champ select screen then rename the mp3 file to:
ChmpSlct_BlindPick For blind pick champ select screen
ChmpSlct_DraftMode For Draft mode champ select screen
ChmpSlct_Tutorial For Tutorial champ select
3. Copy the renamed mp3 file and go to League of Legends\air\assets\sounds\ambient
4. Paste the copied mp3 file, overwriting the original file.
5. Enjoy your favorite music in login screen/champ select.