Emily asked Nora to not tell anyone about her situation, including Richard. However, considering the current situation Nora has no other way rather than relying on someone whom she thinks is reliable.
That's why, after gaining permission from the headmaster that she wanted to check on Emily, she took a day off and came here using Teleportation.
She knew lying was not good, more so when the Headmaster had so many eyes and ears all around Eldoria, but she didn't have any option. If she had said she wanted to meet Richard, the Headmaster would have asked her the reasons. And using his tricky way of conversation he would have found out about the whole thing relating to Emily and Ethan.
So yes, lying was the only option.
Now, sitting inside the mansion she was feeling inexplicably nervous. The possibility of Richard not having any solution to Emily's situation or for him to deny helping his ex-fiancée—which wouldn't be unreasonable—was quite high.