Here’s a link to the original lyrics, and, as advertised, a lyricized English translation that’s very close to the original German.
What I’d like, though, is a more literal translation, one that doesn’t try to fit it into a rhyme scheme or poetic measure.
Vor der Kaserne
Vor dem großen Tor
Stand eine Laterne
Und steht sie noch davor
So woll’n wir uns da wieder seh’n
Bei der Laterne wollen wir steh’n
|: Wie einst Lili Marleen. 
Well, you know much of this is idiom and shouldn’t be translated word for word, but I’ll try.
first verse:
In front of the barracks
In front of the great door
Stood a lantern
And if it’s still standing there today
Then there we’ll see each other again
By the lantern we will stand
As once Lili Marleen…
Actually, now that I compare this first verse I translated with the page you cited, the “fairly literal” translation, is about as literal as you’re going to get without translating word for word. I’m not sure what you’re after, or why you don’t like that version, but no language can be translated word for word without sounding utterly stupid (like my translation above). I won’t bother with the rest, be assured the translation on the page is pretty close.
Aw, what the heck…
Both of our shadows
Looked like one
That we loved each other very much
Was obvious (One could tell right away)
And everyone should see
When we stand by the lantern
As once, Lili Marleen
Then the guard calls:
They are playing Taps
That can cost three days
Comrade, I’ll come right away.
Then we said farewell
How I’d like to go with you
With you, Lili Marleen
Out of the still space
From the earthly ground
I am lifted like in a dream
By your loved mouth
When the late mists swirl
I will stand by the lantern
As once, Lili Marleen
See what I mean?
Thanks! That pretty much does it.
That isnt quite accurate; a better interpretation would be
I like big butts and I cannot lie
You other brothers just can’t deny
That when a girl walks in with an itty bitty waist
And a round thing in your face
You get sprung…
I think that’s as far as I can go by board policy on copyright and fair use.
I believe it was written by `Herr Mix-A-Lot.’