I think this is all about
the movie The Good, The Bad, and The Ugly.
A fair-haired small rodent with cherubic gaze
This seems to be all three of the principal characters: Blondie (nickname given to Eastwood's character) is The Good; Tuco, nicknamed The Rat, is The Bad; Angel Eyes is The Ugly.
was cooking string pasta in Occidental ways.
The movie is a spaghetti Western.
A Monegasque prince was the person who pays,
metallic drugs brought each man to a haze.
I confess I'm not sure what any of this is about. The actress Grace Kelly was a Monegasque princess but doesn't seem to have had anything to do with the movie. There are some people who pay other people but so far as I can tell none of them is a prince, or called "Prince", or anything to do with Monaco. I suspect I'm missing something. "Metallic drugs" seems like it ought to mean money, which can have powerful effects on the mind, especially given that TGTBATU and its two predecessors are collectively known as "the Dollars trilogy", but if there's any specific reference here I'm missing it. (I haven't seen any of these movies.) [EDITED to add:] SteveV informs us in comments that the surname of the movie's producer, Alberto Grimaldi, is the name of the House of Grimaldi, which among other things is the royal family of Monaco.
An evil Italian lion strolled in,
I think "evil" is a nod to "The Bad" in the title; Sergio Leone was the director.
followed at once by a virtuous duckling.
Again "virtuous" refers to "The Good" in the title; perhaps "duckling" is alluding, via the story of the Ugly Duckling, to the last element of the title?
From Easterly forests the info came in,
a somber knoll holds some great treasures within.
There's $200,000 buried in a grave in Sad Hill cemetery.
A Latin American impasse ensued,
confronting each other in three-person feud.
A three-way Mexican standoff occurs, as in many spaghetti Westerns.
A serious one-metre place by them all viewed,
The cemetery court_yard_ where the Mexican standoff takes place? [EDITED to add:] SteveV suggests in comments that this is referring to the grave, but surely that would be larger than one metre?
everyone eyed the anonymous dude.
At the end of the movie, The Man With No Name (Clint Eastwood's character in the trilogy of which this movie is the third, also known in this one as "Blondie") rides off into the sunset. I don't know whether everyone eyes him, but Tuco watches him go. Or perhaps this is still about the Mexican standoff. [EDITED to add:] SteveV suggests in comments that the anonymous dude might be the occupant of the grave (which is labelled "Unknown") ... but isn't the grave actually empty apart from the money?