I was wondering when you’d post when I was typing that. And I was expecting you to suggest Lay Down You Weary Tune as well. 
j
“Lay Down Your Weary Tune” is a fantastic song, especially the Byrds’ version, but I’m not good at questions like “come up with songs starting with an ‘L’”, so I didn’t think of it.
And I have to add my support for “Lola”. IMHO, the Kinks made one of the best pop songs ever, “Waterloo Sunset” (not starting with an ‘L’) as well as one of the best rock songs, “Lola”. It has everything.
Luck Be A Lady / Sinatra
Love To Love / UFO
Love Reign O’er Me / The Who
Not to be confused with Letter B by The Beetles
Leaving on a Jet Plane by John Denver.
I reserve my right for two more selections later on.
I’m another Lola fan. The rare song that I’ve heard a million times and still like.
Legs- ZZTop
Land of Confusion- Genesis
Lets Go Crazy- Prince
Nearly every one I can think of has been mentioned except:
Lather/Jefferson Airplane
Plenty I’d mention have already come up, so I’ll just add a few more:
Livin’ on a Prayer - Bon Jovi.
Let Her Cry - Hootie and the Blowfish.
Little Lion Man - Mumford and Sons.
(figured I’d add a bit more from the 80s, 90s, 00s)
As much as I like “La Bamba”, should it be disqualified due to 'La" being an article?
Ni lo sueñes! Ni hablar! …
Carajo! Stupid Wikipedia agrees with you:
First three that came to mind:
“Life’s Been Good” – Joe Walsh
“Laura” – Billy Joel
“Let It Be” – The Beatles
Now to see the rest of the suggestions…
“Lush Life”–John Coltrane and Johnny Hartman
Lay down beside me- Allison Krause and John Waite
Lilliburlero — Various artists.
Losing My Religion - R.E.M.
Lump - The Presidents of the United States of America
Love Shack - The B-52’s
Adding two more to my prior list, continuing to include some more recent options:
Learning to Fly - Pink Floyd.
Land of Confusion - Genesis, although I find the Disturbed cover more awesome these days.
Lay It Down, Ratt
Lick It Up, Kiss
Living Loving Maid - Led Zeppelin
Let Me Be There - Olivia Newton-John
Leave It - Yes
and since Lady by Styx has already been mentioned:
Lady - Little River Band
Lady - Kenny Rogers
Lady (You Bring Me Up) - The Commodores
“The Lion Sleeps Tonight” should probably be considered for the list. Many artists; pick your favorite.