Thanks to Looney Tunes and his other animated appearances. He's my primary example of cultural osmosis, where you become familiar with a thing through all the references to it, without ever having seen the ur-thing.

On a morning from a Bogart movie
In a country where they turn back time
You go strolling through the crowd like Peter Lorre
Contemplating a crime
She comes out of the sun in a silk dress running
Like a watercolor in the rain
Don't bother asking for explanations
She'll just tell you that she came
In the year of the cat
She doesn't give you time for questions
As she locks up your arm in hers
And you follow 'till your sense of which direction
Completely disappears
By the blue tiled walls near the market stalls
There's a hidden door she leads you to
These days, she says, I feel my life
Just like a river running through
The year of the cat
While she looks at you so cooly
And her eyes shine like the moon in the sea
She comes in incense and patchouli
So you take her,…








Source: LyricFind

And I belatedly learned it's not the only song to reference Peter Lorre.