In opera you're allowed to do anything. In general directors should try to remember that the person is going to be singing, but they put them into just about any position. I've never seen anyone singing standing on their head, but that's about the only pose I can think of that I haven't seen. Lying down is popular. Front and back. Singing in the bathtub. Anything.
Recitals are something else entirely. Liszt started the tradition where the pianist plays in profile. He had a really great profile when he was young and wanted to show it off. So maybe the pianist has to be playing in profile before the singer starts standing in the crook of the piano. This is tradition. You can put your hand on the piano, but not all the time. You can fold your hands together, but not all the time. You can take a little step forward. You can gesture as long as you don't get too carried away. But that's pretty much it.
Cecilia Bartoli has been known to choreograph in her piano recitals. When she is doing the French song where she pretends to be a ladybug, she holds her hand out like the ladybug is her hand talking.
But the kind of elaborate movement suggested by Lotte Lehman is really more than we're used to seeing. Anything that gets you thinking about the song is bound to be an improvement. What is this song about? How does it make me feel? If the answer to this last question is nothing, find another song to do. If you always get this answer, take up another profession.
The key is the right action that creates the right feeling.