I won't add to what's already been suggested, but I also had a lotus birth.
My placenta was delivered with the baby and wrapped up with her. It was not cut or clamped. I held them both until I couldn't cope with the claustrophobia in theatre (but that's my own issue) and then DH held her.
We then unwrapped her and had skin to skin in recovery and I clamped and cut the cord myself.
If you know you don't deal well with particular drugs (for me it's morphine and it's derivatives) - tell the anaesthetic staff, and make sure they are aware.
If you do get claustrophobic don't allow them to strap your arms down. My Ob applauded me for saying something.
I did request a maternally assisted birth but the hospital I went to had quite a high infection rate, and I was then happy to have the lotus birth instead of possibly compromising my health and my ability to look after bub.

HTH some.