To sum up: no, there is no way to fix the error since it is not our fault, but the developers’. But if you want to find out why it happens and even predict its next occurrence, walk with me.
What is Error 39?
This error code is related to connection problems with the game servers. In this case, some players cannot enter a match and others are prevented from even logging in. Usually, this error occurs when there are updates to be made to the game, as happened recently with the arrival of Episode 2, Act II. In these cases, there is not much that can be done, that is, players should wait for the downtime of the servers to end. To be sure that it is the game server’s problem and not your connection, you can check the server status. There is a dedicated tool from Riot that you can analyze the seriousness of the situation. If there isn’t a report there, you can rest assured that the problem will be solved quickly. If your anxiety is on red alert and you can’t wait to rise your ranks, there is another tool to analyze server problems. DownDetector not only shows the current situation but also the last 24-hour report. There is a small chance that it is a problem with your internet. At the risk of sounding like an amateur ISP support, you can reset your router or the client, or even your PC, and then try again. Or just watch Netflix in the meantime. Fortunately, Riot is a big-ass company and always tries its best to solve the problem in the shortest possible time.