Can I lay my PC on its side?

Solution
As long as everything is mounted correctly, yes. Make sure you have the component side of the motherboard facing toward the sky so gravity isn't working against any installed cards or GPUs.
They don't call them DeskBottoms for a reason. The PC really doesn't care what orientation it is in at all. But under the desk is a bad spot because of heat and dust.

That said, you can have your computer set up however you'd like! it won't care as long as it doesn't get too hot.