Q:

What was the Lost Ones first appearance, Azeroth or otherwise? 

I have been curious about the Lost Ones (mutated Eredar/Draenei) ever since I first stumbled upon them.   Have they made any appearances in any canon stories previous to World of Warcraft time-frame?   

A:

Yes, their first appearance was in the Warcraft III: The Frozen Throne Alliance campaign where Prince Kael'Thas and his Blood Elves journeyed to Outland with Illidan and the Naga. 
They were simply referred to as "Draenei" and their leader was Akama (whose shade is currently a WoW boss in the Black Temple raid).  Their appearance was quite similar to how the Broken currently look, with long, thin teeth and they spoke in "whisper"-sounding voices.  Every Draenei had the ability of permanently invisibility.  One of the missions involved infiltrating Hellfire Citadel to bring down Magtheridon, who was also a 25-man raid boss in WoW:BC, and you commanded three armies (Blood Elves led by Kael'Thas, Draenei led by Akama, and Naga led by Lady Vashj) to do a multi-pronged attack on the citadel and its fel orcs and demons.  The Draenei used their stealth abilities to sneak past the fortifications and take out power generators to disable the demonic contraptions that guarded the walls. 
Maeiv and her Night Elf Watchers also chased Illidan to Outland for vengeance, and both Maeiv and Akama both play parts in the Black Temple story in WoW. You can even meet their NPC's as part of the Ashtongue Deathsworn Faction in Shadowmoon Valley, and in certain encounters in the actual Black Temple Raid. 
Unfortunately, when the Burning Crusade WoW expansion was released, Blizzard did quite a big lore shift (Blizzard even admitted later this was a large mistake or ret-con, citation needed) and the Draenei were prettied up to be an peaceful, Alliance-playable, holy-magic wielding race and it was explained that Akama and his other Draenei were in fact members of the "Broken" Draenei sub-race.  Interestingly enough, Draenei do not have the Rogue class available to them, despite that all Draenei were permanently invisible in the Warcraft III campaign. 
It was also mentioned that the Draenei co-existed with the orcs on Draenor (Outland) until the Orcs consumed fel blood and began slaughtering the Draenei. 
I can't cite sources because I am at work, but feel free to look it up on WoWWiki and play the Warcraft III: TFT campaign if it is available to you.  I am just recalling this information off the top of my head so if anyone knows the details better, please correct me! 
Edit: According to the additional lore added, the Prophet Velen (the current leader of the Draenei in WoW) was quite literally "bros" with both Kil'Jaeden (an overarching force of evil throughout the Warcraft III campaigns, and the final boss of Sunwell Plateau raid) and Archimonde (a demon summoned by Kel'Thuzad during the Warcraft III original campaign to destroy Azeroth by consuming the Nordrassil, the world tree on Mount Hyjal.  He also appears in the Caverns of Time: The Battle for Mount Hyjal raid in WoW), both of whom are Eredar demons.  If someone please could look up the relation between the Eredar and Draenei races for me it would be a great addition to this question. 

A:

I summed this up in a comment on Lotus' answer last month, but I decided to add a whole new answer with more up-to-date information. 
We first see The Broken in WarCraft III during the journey to Outland.  However, it's only as of the latest WoW expansion - Warlords of Draenor - that we now have a complete picture of the Draenai culture.  The expansion takes us to an alternate version of Draenor in which the events of the first three WarCraft games never happened (from Draenor's perception, that is). 
The Exodus from Argus
When Sargeras first turned on the Titans, he began looking for a race which could serve as the leadership for the new Burning Legion he was starting.  He found this race in the Eredar - a race of highly-intelligent magic-users on the planet Argus.  He approached the ruling council (family?)  of Argus - three brothers who were wise & powerful - and offered them enhanced powers & abilities in return for their service.  Two of the brothers accepted his offer and took the names "Archimonde" and "Kil'jaeden".  The third brother, Velen, refused and quickly found himself on the wrong side of the new Burning Legion leadership.  As a result, he and his followers - those who refused to serve Sargeras - fled Argus in a gigantic citadel ship along with the light-beings called Naaru.  After several years of searching, they crashed on a planet which housed several sentient races (Orcs, Ogres, and Arrakoa).  These refugees from Argus called themselves "Draenai", which means "exile" in their tongue.  They called their new home Draenor, and sought to live in peaceful co-existence with the other races there. 
The Second Exodus
Centuries later, after the Draenai had been living in peace with the Orcs for generations, the orcs made a pact with the Burning Legion.  Upon learning of the Draenai, the Legion immediately made it a priority to wipe them out.  After fighting a losing battle for several years, Velen led a few thousand of the Draenai to infiltrate the remains of the old citadel ship (now called Tempest Keep) and steal one of the five life-ships that comprised it (the sixth had originally crashed into Nagrand and became Oshu'gun, but was no longer functional).  With only a single Naaru to guide them, the ship's performance was less than optimal, later crashing into the Blood Isles on Azeroth and becoming the city of Exodar. 
The Broken
In addition to the campaign against the Draenai, the orcs began constructing a large portal to Azeroth, the ultimate objective of The Burning Legion.  The orcs' invasion of Azeroth then resulted in an alliance of races from THAT world invading Draenor in kind.  As a result of the Alliance invasion, one of the Orc warlocks - Ner'Zhul - tried to flee Draenor by opening numerous portals into The Twisting Nether.  The energies from the multiple portals could not be controlled, and as a result Draenor was twisted and shattered into a remnant of its former self which came to be known as "Outland".  The remaining Draenai on the planet were caught in these energies and twisted as well, becoming misshapen versions of their former selves called "The Broken".  When the Dark Portal opened again years later, some of the Broken managed to flee through it to Azeroth.  Separated from the other Broken and outcasts to the Draenai on Azeroth, these individuals called themselves "Lost Ones". 
Alternate Draenor
The alternate version of Draenor featured in "Warlords of Draenor" shows us how the war between the Draenai and the Orcs might have occurred WITHOUT the interference of the Burning Legion.  Even with the assistance of Garrosh Hellscream and the Goblin technology he brought with him, the orcs are finding the campaign against the Draenai to be difficult, whereas in the original timeline it was essentially a one-way slaughter. 
On this version of Draenor, we meet the most famous Broken - Akama - in his original form.  Here he is still an Exarch of the Draenai people and one of their most prolific leaders.  No Broken are present on this version of Draenor since the fel energies that originally twisted them have not been released... yet.  Given the demonic nature of Gul'dan and Nerzhul's power, that may change.