"Let's Fall In Love" is a song written by Harold Arlen and Ted Koehler and published in 1933. The major hit at the time of introduction was by Eddy Duchin. It was originally written in C major with a "Moderately Bright" tempo marking. As a jazz standard, it's usually played with a medium swing beat.
Other Notable Recordings

The film It Should Happen to You (1954) uses the song as the central love theme between Jack Lemmon and Judy Holliday, who sing it several times interspersed with dialogue, and hum it together at the end.
Ella Fitzgerald - Ella Fitzgerald Sings Sweet Songs for Swingers (1959), accompanied by the Frank De Vol Orchestra. She recorded it again with Billy May and a full orchestra for "Ella Fitzgerald Sings the Harold Arlen Songbook"(1961).
Shirley Bassey - Let's Face the Music (1962)
It also appeared in the movie Plots with a View.
Soul duo Peaches and Herb revived the tune in 1967.
Carl Riseley - "The Rise"
Diana Krall - When I look Into Your Eyes (1999) and Live in Paris(2002)
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Lyrics

I have a feeling, it's a feeling, I'm concealing, I don't know why It's just a mental, sentimental alibi

But I adore you So strong for you Why go on stalling I am falling Our love is calling Why be shy?

Let's fall in love Why shouldn't we fall in love? Our hearts are made of it Let's take a chance Why be afraid of it

Let's close our eyes and make our own paradise Little we know of it, still we can try To make a go of it

We might have an end for each other To be or not be Let our hearts discover

Let's fall in love Why shouldn't we fall in love Now is the time for it, while we are young Let's fall in love

We might have and end for each other To be or not be Let our hearts discover

Let's fall in love Why shouldn't we fall in love? Now is the time for it, while we are young Let's fall in love (4x)