No, you wouldn't have to have taken the lid off, because one of the thermostats is a non re settable type, so if either boiler gets too hot, the machine powers down as you were seeing . It is not resettable, but power would resume once the machine has cooled down below the thermostat threshold. You can see in the video linked earlier that they have not used two resettable thermostats . They had issues with bad temp probes, and this was their solution . There is nothing in the LCC to shut it down if temps get too high
Either way - good to see your machine is working fine now.

What's an "LCC"?

LCC = Lelit Control Center. Is the PID and more screen. That is how Lelit Describes it

digital display and settings control unit on front of the machine.

"Liquid Crystal Controller"?

previous poster was correct with Lelit Control Center but sure, that works too. maybe Lelit is open to a change.

I suggest that we encourage the use of the more generic term, PID when referring to these . Lelit Control Centre indeed; sounds more like something in an industrial complex