I'm going to be honest...
I had no idea about 'lateral' but I looked it up at dictionary.com. I think, in this context, it means a side-table. I would never say 'lateral table' though. Perhaps it is British? It would be a small table that is positioned beside a sofa/couch.
Spandex - I have no idea. This is only used in terms of clothing or fabric. I think this is a mistake. Perhaps they want a low table with a white plastic top?
An ottoman is a footstool, usually padded and plush, in the USA. It can also be a low cushioned seat or sofa.