Don't lie on that spot, get off please.
Here, on that spot sounds off, though it's technically correct. It's better if you could just directly mention what that spot is.
Don't lie on that bed/bench. Get off, please.
As for 'Don't step in that spot', it is wrong because you physically can't step in a spot. You can step on it. You can step in dung or something with depth to it. You could also say, don't put me in a spot, but it's not a physical spot we're talking about here.
Generally, you use 'in' where there are depth and bounds, and 'on' when there is more free space, in this context. That's why we use 'sit on a sofa' because there's always additional space after one sits on a sofa. If it's an armed chair, we use sit in that chair, but if it's an arm-less chair, we use sit on a chair. We say in the kitchen because it has bounds. We say in the cricket ground if the ground has clearly defined limits. We say on the playground if the ground doesn't have visible limits like when children play on the village-side grounds.
So if that spot you're talking about has depth and bounds, then you can say, 'Don't swim in my pool, get out please.' Streets, or beds, etc can get the preposition 'in' depending on the context.
He's walking on the street means you're generally walking on that street without much importance to anything else.
He is walking in the street means, you're hinting that the street is busy with traffic.
Sleeping on the bed means plainly sleeping without covers.
Sleeping in the bed means sleeping under covers.