In modern times, when one hears about the "Aramaic Lord's Prayer," the most likely source is the tradition found in the Syriac Peshitta.

Interesting note: Be careful where you use the world "Peshitta" on the internet. Because it contains a certain 4-letter euphemism for excrement, it often falls victim to the Scunthorpe Problem, and may get you in trouble with profanity filters.
To Begin
So what is the Peshitta? Good question.

The Peshitta, is a Bible tradition written in Classical Syriac Aramaic that was the actually two separate works . . .

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