I agree with you. We don't typically use "Lass" alone. We say
All of these convey the meaning of "don't do it". The last one is much more friendly and also applies to situations where we want to reject a positive offer:
Ich geb einen aus!
Lass mal, ich bin dran!
The second one has the most scolding undertones. Mothers use it quite a lot scolding infants.
We have some more forms:
Lass es bleiben!
Lass es sein.
Personally, I use the first of them to discourage actions in the future:
ich wollte mir Aktien kaufen!
Lass es bleiben, das hat schon manchen ruiniert!
I was unsure whether to add it, because I heard it relatively recently, extremely seldom and in a peculiar, very colloquial context, but I can confirm that I have heard
"Lass mal stecken"
from a native speaker.
Using "lass" on its own may indicate hasty speech or a non native speaker.
I agree that "Lass" alone sounds acceptable when directed at a dog. That still doesn't render it idiomatic German. Furthermore, would never use it on a child. The association would be treating it like a dog!
There are plenty of things you can say to a dog which are not standard German. For example "Leg!", when you wish it to lay down something. However, even after this experience, I shall never include such language in my explanation, if it is not explicitly requested.
I can see "Lass" working with a dog, but I would never use it myself. "Halt", "Sitz","Stop", all make natural choices, without keeping me waiting for the end of the sentence.
In response to the down votes, I want to make it a little clearer, why it sounds unnatural and incomplete to me. If I say:
nobody is left left waiting for a completion. Hence, "komm!" is absolutely natural.
On the other hand, if I say:
nobody will be able to point to any meaning. That does not mean that a German native speaker could fail to understand that "lass!" meant "lass es". It just means, that it is a similar class of "sentence" as
Mama mamm, mamm!