How can I fetch lyrics for all my music and store them within the files?

This is a semi answer as I don't know your environment and the code I provide is intended to serve as an example only - running it as is shouldn't do any harm but I can't give any guarantee.

Tasks like this can be dealt with using simple bash scripts, e.g. in the following example I use eyeD3 to extract artist and title, then a free wikilyrics mirror to fetch the lyrics and then eyeD3 again to save the new tag. I encourage every one who will use this code to look up another lyrics API, as exploiting the same service over and over can be considered malicious.

#!/bin/bash

_TPL='http://makeitpersonal.co/lyrics?artist=<artist>&title=<title>'
_SRY="Sorry, We don't have lyrics for this song yet."

[ "$1" ] && _PATH="$1" || _PATH=$PWD

cd $_PATH

for _FILE in {*.mp3,*.m4a}; do
    if [[ -r $_FILE ]]; then
        _SONG=$(eyeD3 --no-color "$_FILE" | grep title)

        _ARTIST="${_SONG#*"artist: "}"
        _TITLE="${_SONG%"artist: "*}"
        _TITLE="${_TITLE#"title: "}"

        echo -n "$_ARTIST - $_TITLE"

        _ARTIST="${_ARTIST// /+}"
        _TITLE="${_TITLE// /+}"
        _URL="${_TPL//"<artist>"/$_ARTIST}"
        _URL="${_URL//"<title>"/$_TITLE}"

        _LYRICS=$(wget -qO- $_URL)

        if [ "$_LYRICS" != "$_SRY" ]; then
            eyeD3 --lyrics=eng:Lyrics:"$_LYRICS" "$_FILE" 1>/dev/null
        else
            echo "No lyrics found... skipping!"
        fi
    fi
done

cd $OLDPWD

Instructions (run commands in terminal):

1. install wget and eyeD3 by issuing sudo apt-get install wget eyed3
2. save above code to a file, e.g. /home/user/lyrics_fetcher.sh
3. add permission to run the file: chmod u+x /home/user/lyrics_fetcher.sh
4. run the file (mind the quotes): /home/user/lyrics_fetcher.sh "path_to_my_album"
5. you can stop script execution at any time by pressing ctrl+c

I checked this code with "AM" album by Arctic Monkeys and it did sweetly.

If you really want to fetch lyrics for all of your albums at once you can run the script in a loop for each directory, I guess. Still, I wouldn't use it as a final solution - wikilyrics and everyone who supports it by mirroring are good guys and this answer is here to promote thinking, not abuse.

I recently wrote a python script for Automatically fetching and tagging lyrics to your music. Check it out here. This will download the lyrics as txt file and embed it in your .mp3 file

Youtube Demo.