Disc One (track number to the left)
1	Opening credits
1	Prologue - Ringwraith Theme
1	Gollum takes the Ring into the MM
3	Gandalf arrives in the Shire
7	Bilbo leaves the Shire
7	The Nine ride from Minas Morgul
7	Isildur's Account of the Ring
7	Merry and Pippin Drinking Song
10	Frodo and Sam spy the Wood Elves
11	The Wizards fight at Isengard
12	Ringwraith chases the Hobbits
14	Ringwraiths enter Bree
14	Aragorn sings in the Marshes

Scene: Opening credits
CR-FOTR Track: Prologue: One Ring to Rule Them All; 1-1
Source Text: Footsteps of Doom, Lament for Gandalf, chorus
verified by symphony lyrics - hidden text 

[00:06] Man
[00:09] Ammen
[00:10] Toltha
[00:11] I
[00:12] Dann
[00:13] hen
[00:13] Morn
[00:19] Si
[00:21] Danna-
[00:23] (a drawn out) tha
[00:24] Nauva

Scene: Prologue - Orc Army attacks the Last Alliance - Sauron attacks the Last Alliance

CR-FOTR Track: Prologue: One Ring to Rule Them All; 1-1

Source Text: Revelation of the Ringwraiths

verified by symphony lyrics - hidden text

[2:18] nênâ-
[2:20] kham nêpâm
[2:24] (a)bârat
[2:26] aglar
[2:29] nêbâ
[2:31] katharâd
[2:34] Nidir
[2:37] nênâ
[2:40] nêbâ
[2:41] bî
[2:42] thâm (dâ)ur

[3:00] nênâ
[3:03] kham nêpâm
[3:05] (a)bârat
[3:08] aglar

Scene: Prologue - Gollum takes the Ring into the Misty Mountains (voice over shot of Misty Mountains)
CR-FOTR Track: Prologue: One Ring to Rule Them All; 1-1
Source Text: The Prophecy 
verified by symphony lyrics - hidden text 

[5:33] Ter
[5:35] cá
[5:37] no
[5:39] Nu
[5:41] ru
[5:43] va
 

It is the same as the (mostly unused) music heard on the regular FotR soundtrack CD, track 1, The Prophecy which certainly uses singing. The Annotated Score, however, does not list "The Prophecy" as a source text. 

Scene: Gandalf Arrives in the Shire 

CR-FOTR Track: Bag End; 1-3

Source Text: The Road Goes Ever On

[0:05 - 0:28]

(humming)
Down from the door where it began.
(humming)
And I must follow, if I can,

The Road goes ever on and on
Down from the door where it began.
Now far ahead the Road has gone,
And I must follow, if I can.
  

Scene: Bilbo Leaves the Shire
CR-FOTR Track: Keep It Secret, Keep It Safe; 1-7
Source Text: The Road Goes Ever On 

[3:49 - 4:06]

The Road goes ever on and on
Down from the door where it began.
Now far ahead the Road has gone,
And I must follow, if I can.

Scene: The Nine ride from Minas Morgul 
CR-FOTR Track: Keep It Secret, Keep It Safe; 1-7
Source Text: Revelation of the Ringwraiths 
verified by symphony lyrics - hidden text 

[06:23] Nêbâ
[06:25] bîtham
[06:27] Magâ
[06:29] nanê 

The FOTR Annotated Score says that the Seduction of the Ring can first be heard in Disc 2, Track 10 (Boromir's Seduction on Caradhras). But  the lyrics here are from the Seduction of the Ring.

Scene: Merry and Pippin Drinking Song at the Green Dragon Inn

CR-FOTR Track: Keep it Secret, Keep it Safe; 1-7

Source Text: Hey, Ho! To the Bottle I Go

[8:29 - 8:52]

Hey ho! To the bottle I go
To heal my heart and drown my woe
Rain may fall and wind may blow
But there still be
Many miles to go
Sweet is the sound of the pouring rain
And the stream that falls
From hill to plain
Better than rain or rippling brook
Is a mug of beer inside this Took 

Scene: Frodo and Sam spy the Wood Elves
CR-FOTR Track: The Passing of the Elves; 1-10
Source Text: The Passing of the Elves 

[00:00] Fanuilos heryn aglar
[00:10] Rîn athar annún-aearath,
[00:20] Calad ammen i reniar
[00:30] Mi ‘aladhremmin ennorath!
[00:40] A Elbereth Gilthoniel
[00:50] I chîn a thűl lin míriel
[01:00] Fanuilos le linnathon
[01:09] Ne ndor haer thar i aearon.
[01:20] A elin na gaim eglerib
[01:30] Ned în ben-anor trerennin
[01:39] Si silivrin ne pherth ‘waewib
[01:48] Cenim lyth thílyn thuiennin.
[01:58] A Elbereth Gilthoniel
[02:08] Men echenim sí derthiel
[02:17] Ne chaered hen nu ‘aladhath
[02:27] Ngilith or annún-aearath.

Scene: The Wizards fight at Isengard
CR-FOTR Track: Saruman the White; 1-11
Source Text: The Black Speech Ring Verse 
verified by symphony lyrics - hidden text  

[03:24] Ash Burz-Durbagu
[03:28] Burzum ishi
[03:31] Daghburz-ishi
[03:35] makha
[03:39] gulshu darulu
[03:44] Ash
[03:46] Burz
[03:48] dur-
[03:50] ba-
[03:52] gu
[03:54] bur-
[03:57] zum
[03:59] i-
[04:00] shi
 

Scene: Ringwraith chases the Hobbits
CR-FOTR Track: A Shortcut to Mushrooms; 1-12
Source Text: Revelation of the Ringwraiths 
verified by symphony lyrics - hidden text

[01:47] nê
[01:50] bâ
[01:53] bî
________

[03:12] Nêbâ
[03:15] bîtham
[03:16] magâ
[03:18] nanê
[03:22] Bârî’n
[03:24] ka(tharâd) Ni
[03:26] dir
[03:28] nênâ
[03:30] dâur-ad 

Scene: Ringwraiths enter Bree

CR-FOTR Track: The Nazgûl; 1-14

Source Text: Revelation of the Ringwraiths 
verified by symphony lyrics - hidden text

[00:55] Bârî
[00:57] 'n Katharâd
[01:00] Îdô
[01:03] Nidir
[01:06] nênâ
[01:08] kham nêpâm
[01:11] bârat
[01:14] aglar

Scene: Aragorn sings in the Marshes

CR-FOTR Track: The Nazgûl; 1=14

Source Text: The Song of Lúthien

[04:36] Tinúviel
[04:41] elvanui
[04:45] Elleth alfirin
[04:49] edhelhael
[04:53] O hon ring
[04:56] finnil fuinui
[05:01] A renc gelebrin
[05:05] thiliol