"The minute you put a song over the titles or in any part of the picture, you're unconsciously trying to play on the viewer's pocketbook - you're trying to get him to listen, to go out and buy."
--   Henry Mancini

For most of his scores for motion pictures, Henry Mancini wrote at least a song for them, with the lyrics by well-known songwriters like Johnny Mercer, Hal David, Livingston & Evans and many more. 
Here I will present the lyrics I could find, but I am looking for them everywhere so check it from time to time. I might even try to transcribe some of them myself ...
 
This is a listing of the lyrics of all the songs that I have.
Please don't ask me for a particular lyric that is not here. If I have any lyrics, I will post it here.

          99 and 44/100% Dead! - Easy, Baby           
          Bachelor in Paradise - Bachelor in Paradise
          Breakfast at Tiffany's - Moon River
          Charade - Charade
          Dear Heart - Dear Heart
          Darling Lili - Overture - Whistling Away the Dark - The Little Birds - The Girl in No Man's Land
             I'll Give you Three Guesses - Smile Away Each Rainy Day - I'll Give you 3 Guesses (reprise)
             Skal - Your Good-Will Ambassador - Whistling Away the Dark (reprise)
          Days Of Wine and Roses - Days Of Wine and Roses
          Hatari ! - Baby Elephant Walk
          Moment to Moment  -   Moment to Moment
          More Music from Peter Gunn  -  Dreamsville
          Mr. Lucky  -  Theme from Mr. Lucky
          Rock, Pretty Baby  -  Free and Easy  -  What's It Gonna Be ?
          Soldier in the Rain  -  Soldier in the Rain
          Summer Love  -  To Know You is To Love You
          Sunflower - Sunflower (Loss of Love)
          Ten  - He Pleases Me - It's Easy to Say - Don't Call it Love - Get It On - I Have an Ear for Love
          The Great Race - The Sweetheart Tree - He shouldn’t-a, Hadn’t-a, Oughtn’t-a swang on me
          The Great Mouse Detective  - Goodbye too Soon - Let me be good to you - 
             The World's Greatest Criminal Mind
          The Party - Nothing to Lose
          The Pink Panther - It had better be tonight - Meglio Stasera
          The Thorn Birds   -  Anywhere the heart goes (Meggie's Theme)
          Two for the Road - Two for the Road
          Victor Victoria  - Paris by Night - If I Were a Man - Trust Me - Le Jazz Hot - 
             Paris Makes Me Horny - Crazy World - Louis Says - King's Dilemma - You and Me -
             Almost a Love Song - Chicago, Illinois - Living in the Shadows - Victor Victoria
          Voice in the Mirror  -  The Ways of Love
          Wait Until Dark - Wait Until Dark
          What Did you Do in the War, Daddy? - In the Arms of Love 

Other songs not written for motion pictures 

          Lonely Winter 
          Music on the Way
          Slow Hot Wind
          Sometimes sung by The Carpenters

Lyrics added after ...

          Joanna lyrics by Johnny Mercer
          When Snow Falls (Latin Snowfall) lyrics by Heather Metcalf
          After One Kiss (The Soft Touch) lyrics by Ed Heyman
          Phone Call to the Past (Theme for Sam) lyrics by Johnny Mercer - from melody of Gunn... Number One