data.txt

83 <40>1 2012-11-30T06:45:29+00:00 host app web.3 - State changed from starting to up
119 <40>1 2012-11-30T06:45:26+00:00 host app web.3 - Starting process with command `bundle exec rackup config.ru -p 24405`

Main.hs

data Log = Log
  { size :: Int
  , time :: Text
  , message :: Text
  } deriving (Eq, Show)

pLog :: Parser Log
pLog = do
  notFollowedBy eof
  size <- L.decimal <?> "size"
  void (char ' ')
  void (char '<')
  void (some alphaNumChar)
  void (char '>')
  void alphaNumChar
  void (char ' ')
  time <- Text.pack <$> someTill anySingle (char ' ') <?> "time"
  message <- takeRest <?> "message"
  return Log {..}

pLogs :: Parser (Vector Log)
pLogs = do
  logs <- sepBy1 pLog eol
  eof
  return $! Vector.fromList logs

result.txt

Right [Log {size = 83, time = "2012-11-30T06:45:29+00:00", message = "host app web.3 - State changed from starting to up\n119 <40>1 2012-11-30T06:45:26+00:00 host app web.3 - Starting process with command `bundle exec rackup config.ru -p 24405`"}]