I had a similar problem when my Moto G updated to 5.1.
There is now a Phone and Camera shortcut on the Lock Screen.
I am left-handed and open the camera.
With swipe to unlock we just have to avoid swiping diagonally lower down.
Swipe straight up is best. I am used to it now, though I often swipe diagonally, but the camera icon location is hard wired in to my brain so I don't open it now.
I raised a thread on this and apparently there's no way to remove the Lock Screen shortcuts.