Reddit reviews The J.R.R. Tolkien Audio Collection

I don't think there is one where he has read LoTR in its entirety, but this one, narrated by him and Christopher Tolkien, comes pretty close. According to description, the quality of older excerpts is not all that great. Below is a complete listing of chapters read by JRRT and CT [Credit to a reviewer, Anonymouse, on Amazon]:

CD 1: Songs and excerpts from "The Hobbit" and "The Fellowship of the Ring" read by J.R.R. Tolkien (49 minutes)

1. The Hobbit: Chapter 5: Riddles in the Dark (29:49)
   
2. The Fellowship of the Ring: Book I: Chapter I: A Long Expected Party - The Old Walking Song (0:17)
   
3. TFotR Book I: Chapter II: The Shadow of the Past - Verse of the Rings (0:52)
   
4. TFotR Book I: Chapter III: Three is Company - A Walking Song (1:01)
   
5. TFotR Book I: Chapter III: Three is Company - "Snow White! Snow White!" (0:38)
   
6. TFotR Book I: Chapter V: A Conspiracy Unmasked - The Bath Song (0:42)
   
7. TFotR Book I: Chapter V: A Conspiracy Unmasked - Farewell Song of Merry and Pippin (0:28)
   
8. TFotR Book I: Chapter VI: The Old Forest - "Hey! Come merry doll!" (0:38)
   
9. TFotR Book I: Chapter VI: The Old Forest - "Hop along, my little friends" (0:21)
   
10. TFotR Book I: Chapter IX: At the Sign of the Prancing Pony - "The is an inn, a merry old in..." (1:53)
    
11. TFotR Book I: Chapter XI: A Knife in the Dark - The Fall of Gil-Galad (0:25)
    
12. TFotR Book I: Chapter XI: A Knife in the Dark - Song of Beren and Luthien (3:06)
    
13. TFotR Book I: Chapter XII: Flight to the Ford - Sam's Rhyme of the Troll (2:36)
    
14. TFotR Book II: Chapter I: Many Meetings - "They got up and withdrew quietly..." (0:31)
    
15. TFotR Book II: Chapter IV: A Journey in the Dark - Song of Durin (1:43)
    
16. TFotR Book II: Chapter VI: Lothlorien - Song of Nimrodel (1:43)
    
17. TFotR Book II: Chapter VII: The Mirror of Galadriel - Frodo's Lament for Gandalf (0:58)
    
18. TFotR Book II: Chapter VIII: Farewell to Lorien - Galadriel's Song of Eldamar ("Namarie Alatriello naina Loreindesse", Galadriel's Lament in Lorien, spoken version) (0:48)
    
    CD 2: Songs and excerpts from "The Two Towers", "The Return of the King", "The Fellowship of the Ring", and "The Adventure os Tom Bombadil" read by J.R.R. Tolkien (73 minutes)
    
    
19. The Two Towers: Book III: Chapter I: The Departure of Boromir - Lament for Boromir (2:39)
    
20. TTT Book III: Chapter IV: Treebeard - The Long List of the Ents (1:20)
    
21. TTT Book III: Chapter IV: Treebeard - Treebeard's Song (1:15)
    
22. TTT Book III: Chapter IV: Treebeard - The Ent and the Ent-wife (2:15)
    
23. TTT Book III: Chapter IV: Treebeard - Bregalad's Song (0:43)
    
24. TTT Book III: Chapter IV: Treebeard - The Ent's Marching Song (1:09)
    
25. TTT Book III: Chapter VI: The King of the Golden Hall - Lament for Rohirrim (0:37)
    
26. TTT Book III: Chapter VI: The King of the Golden Hall - Gandalf's Song of Lorien (0:25)
    
27. TTT Book IV: Chapter II: The Passage of the Marshes - Gollumn's Song (0:57)
    
28. TTT Book IV: Chapter III: The Black Gate is Closed - Oliphaunt (0:57)
    
29. TTT Book IV: Chapter IV: Of Herbs and Stewed Rabbit - "A little way back along the lake..." (7:39)
    
30. The Return of the King: Book V: Chapter III: The Muster of Rohan - Lament for Theodeon (1:07)
    
31. TRotK Book V: Chapter V: The Ride of the Rohirrim - "Then since we must look for fell deeds..." (8:41)
    
32. TRotK Book V: Chapter VI: The Battle of the Pellennor Fields - Song for the Mounds of Mundburg (1:36)
    
33. TRotK Book VI: Chapter III: Mound Doom - "There at the bend it ws cut deep..." (7:09)
    
34. TRotK Book VI: Chapter V: The Steward and the King - The Eagle Song (0:47)
    
35. The Fellowship of the Ring: Book II: Chapter VIII: Farewell to Lorien - Galadriel's Lament in Lorien ("Namarie Alatriello naina Loreindesse", sung version) (1:27)
    
36. TFotR Book II: Chapter I: Many Meetings - A Elbereth Gilthoniel! (from the Tom Bombadil sessions) (0:16)
    
37. TFotR Book II: Chapter VIII: Farewell to Lorien - Galadriel's Lament in Lorien (alternate spoken version from the Tom Bombadil sessions) (1:05)
    
38. The Adventures of Tom Bombadil - "Old Tom Bombadil..." (6:53)
    
39. TAoTB - Errantry (2:54)
    
40. TAoTB - Princess Mee (1:37)
    
41. TAoTB - The Man in the Moon Came Down Too Soon (3:41)
    
42. TAoTB - Perry-The-Winkle (4:27)
    
43. TAoTB - The Mewlips (1:26)
    
44. TAoTB - The Hoard (3:34)
    
45. TAoTB - The Sea-Bells (5:16)
    
    CD 3: Excerpts from "The Silmarillion" read by Christopher Tolkien (68 minutes)
    
    
46. Chapter 19: Of Beren and Luthien: Part 1 - "The story tells that after the battle in which Morgoth..." (1:37)
    
47. Chapter 19: Of Beren and Luthien: Part 2 - "Then there came a time near dawn on the eve of spring..." (10:31)
    
48. Chapter 19: Of Beren and Luthien: Part 3 - "The story tells that Beren, leaving.." (8:12)
    
49. Chapter 19: Of Beren and Luthien: Part 4 - "In the time when Sauron cast Beren into the pit..." (3:19)
    
50. Chapter 19: Of Beren and Luthien: Part 5 - "The story tells that Huan found Luthien..." (7:53)
    
51. Chapter 19: Of Beren and Luthien: Part 6 - "The story tells that Huan returned to..." (35:16)
    
52. Chapter 19: Of Beren and Luthien: Part 7 and Chapter 20: Paragraph 1 - "It is said that Beren and Luthien returned..." (1:33)
    
    CD 4: Excerpts from "The Silmarillion" read by Christopher Tolkien (60 minutes)
    
    
53. Chapter 8: Of the Darkening of Valinor: Part 1 - "When Manwe heard of the ways that Melkor had taken..." (11:44)
    
54. Chapter 8: Of the Darkening of Valinor: Part 2 - "So the great darkness fell upon Valinor..." (2:47)
    
55. Chapter 9: On the Flight of the Noldor: Part 1 - "After a time a great concourse gathered about the ring of doom..." (14:40)
    
56. Chapter 9: On the Flight of the Noldor: Part 2 - "Now when it was known that Morgoth had escaped from Valinor..." (13:52)
    
57. Chapter 9: On the Flight of the Noldor: Part 3 - "Now Feanor led the Noldor northward..." (17:40)

For a selection of the songs (along with readings of sections of his books), you could look into the recordings that Tolkien made after LotR was written but before publication.

For example, here's Sam's song about the troll.

Edit - Oh, right. Also there's The Road Goes Ever On, a book of sheet music and whatnot for some of the songs that was developed by Donald Swann and officially approved by Tolkien.

FWIW, the audio is available on CD as part of The J.R.R. Tolkien Audio Collection, although the cover art isn't as cool. :-)

I would suggest The J.R.R. Tolkien Audio Collection. She probably doesn't have it already, and it's really cool to hear the actual voices of Tolkien and Christopher Tolkien reading from the legendarium.

If you want to DM me the picture of her bookshelf, I can suggest some books too. There's just so many things she probably already has!

Scroll down to the next page - it specifically references Tolkien reading in his Gollum voice in "The JRR Tolkien Audio Collection". Why here's a copy for you to buy!

This is as good as it gets, I think. There's a full version too, with more discs (I think), but I didn't see it.

http://www.amazon.com/The-J-R-R-Tolkien-Audio-Collection/dp/0694525707

It seems to be in there, according to a review. Of course, that's not helpful for listening now, which is what I would've liked. A youtube search was vain, at least for me.

In this episode of the Prancing Pony Podcast they discuss pronunciation starting at about minute 3:00, including a number of clips of Christopher Tolkien. Around minute 7:30 they discuss and play a clip of Christopher Tolkien reading Túna from the Silmarillion. I believe the recording is part of the J.R.R. Tolkien Audio Collection audio book.

Edit: a link

There's a published recording that includes some Bombadil among other awesome stuff.

Encyclopedic, my ass. He pronounces "Thangorodrim" incorrectly.

/ˌθaŋɡoˈrodrim/

This correction via Tolkien Gateway and Christopher Tolkien's own pronunciation on his reading of "Of Beren and Lúthien" (available here to buy; an unconnected excerpt is here).