For artist name in artist_names list, this will use Genius' API and website to download the info and lyrics (as best can be done with html scraping) into named folders in current directory. Need Geinus API Bearer token as well.

genius_song_scrape.py

import requests
from bs4 import BeautifulSoup
import os, json

base_url = "http://api.genius.com"
headers = {'Authorization': 'Bearer GENIUS_API_BEARER_STRING'}

artist_names = ["Fleet Foxes"]

def artist_id_from_song_api_path(song_api_path, artist_name):
  song_url =  base_url + song_api_path
  response = requests.get(song_url, headers=headers)
  json = response.json()
  artist = json["response"]["song"]["primary_artist"]
  if artist["name"] == artist_name:
    return artist["api_path"]
  else:
    return None

def songs_from_artist_api_path(artist_api_path):
  api_paths = []
  artist_url = base_url + artist_api_path + "/songs"
  data = {"per_page": 50}
  while True:
    response = requests.get(artist_url, data=data, headers=headers)
    json = response.json()
    songs = json["response"]["songs"]
    for song in songs:
      api_paths.append(song["api_path"])
    if len(songs) < 50:
      break #no more songs for artist
    else:
      if "page" in data:
        data["page"] = data["page"] + 1
      else:
        data["page"] = 1
  return list(set(api_paths))

def info_from_song_api_path(song_api_path):
  song_url =  base_url + song_api_path
  response = requests.get(song_url, headers=headers)
  json = response.json()
  return json

def lyrics_from_song_web_path(song_web_path):
  #gotta go regular scraping... come on Genius
  page_url = "http://genius.com" + song_web_path
  page = requests.get(page_url)
  html = BeautifulSoup(page.text, "html.parser")
  [h.extract() for h in html('script')]
  lyrics = html.find("lyrics").get_text()
  return clean_lyrics(lyrics)

def song_ids_already_scraped(artist_folder_path, force=False):
  #check for ids already scraped so we don't redo
  if force:
    return []
  song_ids = []
  files = os.listdir(artist_folder_path)
  for file_name in files:
    dot_split = file_name.split('.')
    #sometimes the file is empty, we don't want to include if that's the case
    if dot_split[1] == 'txt':
      try:
        song_id = dot_split[0].split("_")[-1]
        if os.path.getsize(artist_folder_path + '/' + file_name) != 0:
          song_ids.append(song_id)
      except:
        pass
  return song_ids

def clean_lyrics(lyrics):
  lyrics = lyrics.replace(u"\u2019", "'") #right quotation mark
  lyrics = lyrics.replace(u"\u2018", "'") #left quotation mark
  lyrics = lyrics.replace(u"\u02bc", "'") #a with dots on top
  lyrics = lyrics.replace(u"\xe9", "e") #e with an accent
  lyrics = lyrics.replace(u"\xe8", "e") #e with an backwards accent
  lyrics = lyrics.replace(u"\xe0", "a") #a with an accent
  lyrics = lyrics.replace(u"\u2026", "...") #ellipsis apparently
  lyrics = lyrics.replace(u"\u2012", "-") #hyphen or dash
  lyrics = lyrics.replace(u"\u2013", "-") #other type of hyphen or dash
  lyrics = lyrics.replace(u"\u2014", "-") #other type of hyphen or dash
  lyrics = lyrics.replace(u"\u201c", '"') #left double quote
  lyrics = lyrics.replace(u"\u201d", '"') #right double quote
  lyrics = lyrics.replace(u"\u200b", ' ') #zero width space ?
  lyrics = lyrics.replace(u"\x92", "'") #different quote
  lyrics = lyrics.replace(u"\x91", "'") #still different quote
  lyrics = lyrics.replace(u"\xf1", "n") #n with tilde!
  lyrics = lyrics.replace(u"\xed", "i") #i with accent
  lyrics = lyrics.replace(u"\xe1", "a") #a with accent
  lyrics = lyrics.replace(u"\xea", "e") #e with circumflex
  lyrics = lyrics.replace(u"\xf3", "o") #o with accent
  lyrics = lyrics.replace(u"\xb4", "") #just an accent, so remove
  lyrics = lyrics.replace(u"\xeb", "e") #e with dots on top
  lyrics = lyrics.replace(u"\xe4", "a") #a with dots on top
  lyrics = lyrics.replace(u"\xe7", "c") #c with squigly bottom
  return lyrics

if __name__ == "__main__":
  for artist_name in artist_names:
    #setting up path to artist's directories
    artist_folder_path = "artists/%s" % artist_name
    artist_lyrics_path = "%s/lyrics" % artist_folder_path
    artist_info_path = "%s/info" % artist_folder_path
    if not os.path.exists(artist_folder_path):
      os.makedirs(artist_folder_path)
    if not os.path.exists(artist_lyrics_path):
      os.makedirs(artist_lyrics_path)
    if not os.path.exists(artist_info_path):
      os.makedirs(artist_info_path)

    #only using lyrics since they're saved second
    prev_song_ids = song_ids_already_scraped(artist_lyrics_path)

    #find the artist!
    search_url = base_url + "/search"
    data = {'q': artist_name}
    response = requests.get(search_url, data=data, headers=headers)
    artist_info = response.json()
    for hit in artist_info["response"]["hits"]:
      song_api_path = hit["result"]["api_path"]
      artist_api_path = artist_id_from_song_api_path(song_api_path, artist_name)
      if artist_api_path: #done searching if we found the guy
        break

    if not artist_api_path:
      print "Could not find %s" % artist_name

    #find the song api ids for the artist
    song_api_paths = songs_from_artist_api_path(artist_api_path)

    #print out how many songs we have left
    print len(song_api_paths) - len(prev_song_ids)

    for song_api_path in song_api_paths:
      api_id = song_api_path.split('/')[2]
      if api_id in prev_song_ids:
        continue #don't redo
      full_song_info = info_from_song_api_path(song_api_path)
      song_title = full_song_info["response"]["song"]["title"]
      song_title_path = song_title.replace('/', '_')#.replace(' ', '_').lower()
      song_web_path = full_song_info["response"]["song"]["path"]

      lyrics = lyrics_from_song_web_path(song_web_path)

      lyric_path = "%s/lyrics/%s.txt" % (artist_folder_path, song_title_path)
      info_path = "%s/info/%s.txt" % (artist_folder_path, song_title_path)
      #import pdb;pdb.set_trace()

      #for record keeping purposes
      #print (artist_folder_path, song_title_path, api_id)
      print lyric_path

      with open(info_path, "w") as lfile:
        lfile.write(json.dumps(full_song_info))
      with open(lyric_path, "w") as ifile:
        try:
          ifile.write(lyrics)
        except UnicodeEncodeError as error:
          print error