> but what if it fails to start?

Since you're mentioning opening laptop's lid I assume you mean literally failing to start, as after power cycling. For that, wouldn't simple hitting the power button be enough? It certainly doesn't require keyboard. If you plan to place it somewhere not easily accessible, there is Wake on LAN, which most modern PC motherboards are going to support.

If some maintenance task cannot be done with ssh/tmux, you can always use remote desktop software, in local network even RDP will do. And if something went wrong enough for you to not be able to connect to the server remotely then there is indeed no way around bringing and connecting a spare keyboard and monitor, but events like that should be quite rare normally.