You can easily link your logs up to a Discord webhook and have logs steam to a Discord channel in real time. It's a simple as changing a setting on the dashboard and installing a module in your Garry's Mod server.
The first step to setting up Discord integration with your panel is to head over to your Game Server settings and pick a server you want to add integration for. When editing that server, you will be promoted with a Discord Webhook option, here is where you should place your webhook URL. Once you have saved this change, your Game Server will automatically find this new setting the next time it's restarted.
Due to limitations from within Garry's Mod, a DLL module is required in order to support Discord Integration. You can find Reqwest here, a Garry's Mod module that implements an improved HTTP client. If you are with a hosting company (Like Hexane), the Mod Manager will likely include this package for an easy 1 click install. This is the only dependency for Discord Integration.