When I play for instance the Ravel Concerto for the LH, my Rh sometimes has to hold onto the edge of the piano to balance me. I think this is not necessary but for me it makes me feel more solid and sturdy during acrobatic parts.
Things you worry about, but no one ever talks about.I too tend to put my hand on my lap for some reason. It really relaxes my hand.Has driven all 3 of my piano teachers mad.Don't do it as much anymore as my playing has become more relaxed so the need is not as strong.