An enduring element in LSH storytelling is the "alternate" LSH: a variation on the familiar ("Earth-1") Legion. There may be changes in history and continuity, variations in characters, or even humorous or parodic versions of the Legion.
The Crisis on Infinite Earths was supposed to have merged all alternate Earths into one DC Universe, and we are not supposed to see alternate Earths any more. Zero Hour was supposed to do the same thing. Don't you believe it. Alternate Legions continue to appear.
A word of explanation is in order. I consider the "Basic State" or "original" Legion universe to be the Earth-1 universe that contained the vast majority of Legion stories that appeared in the thirty-year period 4/59 to 4/89 in ADVENTURE, ACTION, SUPERBOY, SUPERBOY & THE LEGION OF SUPER-HEROES, LEGION OF SUPER-HEROES, and TALES OF THE LEGION OF SUPER-HEROES. I have chosen to classify as "alternate" any tale that is not consistent (barring minor inconsistencies) with the "Basic State" universe.
We know from LSH 38 that Superboy is capable of travel between alternate universes, and we can assume that such travel is possible for other characters as well.
Please note that this list does not include the multitude of alternate versions that popped into and out of existence before and during the "End of an Era" storyline. Not even Brainiac 5 could keep track of all of those.

A.0.00. Classic Legion (1960s)
A.0.10. Modern Legion (1970s)
A.0.20. Postmodern Legion (1980s)
A.0.30. Pre-Zero Legion (1990s)
A.1. Variations occurring in the Legion's far past
A.1.00. Superman Blue/Red
A.1.10. Krypton Girl
A.1.20. Bruce (Batman) Kent
A.1.30. Warring Galaxy
A.1.40. Superboy Resigns
A.1.50. Superman's Last Stand
A.1.60. Earth-Byrne
A.1.70. Pocket Universe
A.1.80. Kingdom Come
A.2. Variations occurring in the Legion's present or near past
A.2.00. Mxyzptlk V
A.2.10. Computo Triumphs
A.2.20. Mordru Wins Earthwar
A.2.30. The Dark Man Triumphs
A.2.40. Ferro Lad II
A.2.50. Giffbaum #1
A.2.60. Mordruverse
A.2.70. Giffbaum #2 (Glorthiverse) (Earth-2 ??)
A.2.70.5. Legion on the Run
A.3. Alternate versions of the Legion's future
A.3.00. Adult Legion
A.3.10. Orbital HQ
A.3.20. Legion of Almeer-5
A.3.30. Wildfire's Legion I
A.3.40. Wildfire's Legion II
A.3.50. Legion One Million

B.1. Minor variations in canonical characters
B.1.00. Legion of Super-Traitors
B.1.10. Bizarro Legion
B.1.20. Legionnaires (SW6 Batch)
B.2. Major variations in canonical characters
B.2.00. Legion of Oz
B.2.10. Legionnaires of Avalon
B.2.20. Earth-Zero Legion
B.2.20.2. Emerald Legion
B.2.20.4. Animated Legion
B.2.22. Evil Legion of Mordru & Glorith
B.2.30. Golden Age Legion
B.2.40. Mr. Swan's Kids
B.2.50. Brainiac Adventures Kid Legion
B.2.60. Demon Legion
B.3. Variations involving non-canonical characters
B.3.00. Romo's Pack
B.3.10. League of Superteens
B.3.20. League of Infinity
B.3.30. Legion of Titanic Heroes
B.3.40. Legion of Galactic Guardians 2099 I
B.3.50. Legion of Galactic Guardians 2099 II
B.4. Other super-groups with a Legion connection
B.4.00. Legion of Super-Villains I
B.4.10. Legion of Super-Pets
B.4.20. Legion of Substitute Heroes I
B.4.30. Heroes of Lallor
B.4.40. SCPA (Space Canine Patrol Agents)
B.4.50. Wanderers I
B.4.60. Legion of Super-Villains II
B.4.70. L.E.G.I.O.N. and R.E.B.E.L.S.
B.4.80. Legion of Super-Villains III
B.4.90. Wanderers II
B.4.100. Legion of Substitute Heroes II
B.4.110. Lil' Legion
B.4.120. Workforce
B.4.130. Uncanny Amazers
B.4.140. Heroes of Lallor II
B.4.150. Legion of Substitute Heroes III

C.1.00. Wild World Legion
C.1.10. L.E.G.I.O.N. Archives
C.1.20. Legion of Galactic Guardians 2099 II
C.1.30. Legjam of Super-Heroes
C.2. Appearing in non-DC Comics
C.2.00. Legion of Superfluous Heroes
C.2.10. Legion of Stupid-Heroes
D.1. Cosmic Boy/Rokk Krinn/Polestar
D.2. Saturn Girl/Imra Ardeen
D.3. Lightning Lad/Garth Ranzz/Live Wire
D.4. Triplicate Girl/Duo Damsel/Single Sis/Lluornu Durgo/Triad
D.5. Phantom Girl/Tinya Wazzo/Apparition
D.6. Chameleon Boy/Reep Daggle/Chameleon
D.7. Colosal Boy/Gim Allon/Leviathan
D.8. Invisible Kid/Lyle
D.9. Supergirl/Kara Zor-El/Laurel Gand/Andromeda
D.10. Brainiac 5/Querl Dox/5
D.11. Superboy/Kal-El
D.12. Ultra Boy/Jo Nah
D.13. Star Boy/Thom Kallor
D.14. Shrinking Violet/Salu Digby/Vi/Virus/LeVIathan
D.15. Sun Boy/Dirk Morgna
D.16. Bouncing Boy/Chuck Taine
D.17. Mon-El/Lar Gand/Valor/M'Onel
D.18. Matter-Eater Lad/Tenzil Kem
D.19. Element Lad/Jan Arrah
D.20. Lightning Lass/Light Lass/Ayla Ranzz/Pulse/Gossamer/Spark
D.21. Dream Girl/Nura Nal/Dreamer
D.22. Princess Projectra/Jeckie/Sensor Girl/Sensor
D.23. Karate Kid/Val Armorr
D.24. Ferro Lad/Andrew Nolan/Ferro
D.25. Shadow Lass/Tasmia Mallor/Umbra
D.26. Chemical King/Condo Arlik
D.27. Lone Wolf/Timber Wolf/Brin Londo/Furball
D.28. ERG-1/Wildfire/Drake Burroughs/NRG
D.29. Dawnstar
D.30. Blok
D.31. Invisible Kid II/Jacques Foccart
D.32. White Witch/Mysa Nal/Jewel/Mysa
D.33. Quislet
D.34. Tellus
D.35. Magnetic Kid/Pol Krinn
D.36. Polar Boy/Brek Brannin


