Thanks for all your replies, it's given me a lot to think about. I'm new to Arduino (any programming for that matter) and thought that making some lights flash might be a good place to ease into it - looks like I may have been wrong adding the email part.
To elaborate a bit more, the robot I work with is not Arduino but from a company called Hamilton Robotics.
To answer liuzengqiang's question about alerting a user other than email, it will prompt via a PC screen connected to the robot - so a remote alert would be really handy. It may have other ways to alert a user who is not stood directly next to it - I will have to look into that - but I know that it has the ability to ping an email with said alerts.
I think that I might be asking the impossible, as even if the robot does send an email, there's no way for Rasberry Pi, or nodemcu, or Arduino to know what that message says, am I right in thinking this?
If I moved away from the email idea and could, say, connect to the robot PC via wifi - would this be a better, quicker route to sending an alert?
My beginner's brain is telling me that if the robot sends - for example - an error message to a file on the PC that the Arduino/ Raspberry Pi (or nodemcu) can read from wirelessly, then that might be a better solution. If, of course, it's possible to push that information as soon as it's uploaded to the file...
Apologies for the ramblings, and thanks for the comments and suggestions