Yeah, no. First, that's nowhere near what "doxxing" means. Second, it's not possible to "ddos" someone without knowing their IP address. Thirdly, your ISP would generally block large numbers of connections to your home internet, unless you've specifically told them you're running a service on your internet that would require large numbers of incoming connections at once. Granted, ISPs are shit at it, but it's something. Lastly, a DDoS attack requires knowledge of the IP address (unique to your local connection) that you're trying to DDoS - which is not information someone can get from the League Client or Riot, period.
Keep in mind that a DDoS attack requires quite a bit of resources - either many computers/connections to be able to "connect" from at once, or a large amount of resources and a very high-end internet connection.