can anyone tell me if I can put slate down on top of a lawn without removing the grass first, if I put membrane down on top of grass then the slate
Yes, but put down two layers of membrane, first a weed control fabric then a stronger woven landscape membrane. The reason is that the sharp edges of slate will cut a weed membrane and you will soon get the grass or weeds growing through. The second layer of landscape membrane protects the weed fabric. It's a bit more expensive to do this but it will last many more years. When I did this I also overlapped by a good 6 inches and laid the two membranes at 90 degrees to each other.