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Can those be used interchangeably? These are three examples from the Longman dictionary. I see no essential difference between the cases so I assume you can use any option you like without any reservations (no preposition, 'at', or 'on'). Am I right?
a baby sucking at its mother’s breast
Don’t suck your thumb, dear.
a picture of Lara sucking on a lollipop
The literal and most common meaning of "suck" is to draw into the mouth by contracting the muscles of the lips and mouth to make a partial vacuum. This is the definition that applies in all of your examples.
"Suck" and "suck on" are pretty much interchangeable, and in your latter 2 examples, either could work:
Don't suck your thumb / Don't suck on your thumb.
Sucking a lollipop / sucking on a lollipop.
(although "sucking your thumb" is probably the most idiomatic in that example)
However, when it comes to a baby feeding, it is idiomatic to say "sucking at the breast", because it is as much a statement of their location and position as it is what they have in their mouth. It may even be considered an abbreviation of "suckling", which, as a verb, means to feed (a baby or young animal) from the breast or teat.
As an aside, the expression "suck at" something is also a modern colloquialism meaning that you are "bad at", or "not adept" at something.
