This is the answer I owe you, which I am sure by now will be of no use to you.
Disclaimer: here I answer to my own interpretation of the question. Although this is true for every worldly answer, I felt like writing this warning because of the extent of my freedom of interpretation. Also, because of my limited Mediterranean/European background I might be ignorant of major findings in other parts of the world. So this is the question:
"What were important [...] documents [...] that were thought lost [...] and that led to significant new historic understanding when [...] copies became available [...]?" My emphasis.
First of all what is a document? Is it a written source only? Certainly some frescos or architectures tell us more than certain written documents: are they documents too?
Then: what does it mean to be lost: is it physically lost only? Some interpretations are lost, and hence even though people could read the documents, they would not understand them correctly. Sometimes even very well known documents give us new information when read under a new light.
Let's start actually from this latter point of view.
- A: A negative example: the Holy Bible (HB) and the Hittites (Hs).
Because of the positivistic wave in the XIX century, the HB was often disregarded as a valid historical source by scholars. So nobody gave any importance, among other things, to the apparent discrepancy between different appearences of the people of Heth, sometimes referred to as a small tribe, sometimes as a great kingdom.
However, at the end of the century, it became clear that a big, previously unknown civilization had existed in Anatolia; in 1906 Hugo Winkler discovered at Boğazköy the ruins of its capital, Hattusa, including an archive of more than 10000 tablets. Thus the Bible was right: the small Caananite tribe of the people of Heth was most probably distinguished from the mighty Kittim, as they are now known. Moreover, an empire as powerful as Egypt of Ramses II had gone almost completely lost for 3 millennia.
- B: A positive example (with tragic end). The Iliad was regarded as an epic poem loosely based on ancient wars. Scholars argued that a city of Troy might not have existed, and that the episode was rather a summary of ancient episodes of war, collected into an ... epic story. But some people stubbornly believed in the myth, until one of them, Heinrich Schliemann, discovered the city of the poem in the hill of Hisarlık. Incidentally, the discovery of the H civilization added more weight to the episode narrated in the Iliad. The city of Troy, or Ilium, should in fact correspond to the H "Wilusa". See e.g. this and . Sadly the discovery led to the destruction of a considerable portion of the material, including the Troy of the poem.
- C: Finally, and on a personal note, Herodotus' Histories. You might know how Herodotus' reputation changed over time. In ancient times, because of writers like e.g. Tucidides, the opininon on the historian was negative, because of him citing unverified and de relato sources.
Among the "fantastic stories" were the one about Phoenicians traveling from the Red Sea to Gibraltar, circumnavigating Africa. They found a big river flowing eastwards, a population of small black men and the sun "going to the right". I love that passage, so please forgive the long citation from Book iv of the Histories:
[...] for Libya furnishes proofs about itself that it is surrounded by sea, except so much of it as borders upon Asia; and this fact was shown by Necos king of the Egyptians first of all those about whom we have knowledge. He when he had ceased digging the channel which goes through from the Nile to the Arabian gulf, sent Phenicians with ships, bidding them sail and come back through the Pillars of Heracles to the Northern Sea and so to Egypt. The Phenicians therefore set forth from the Erythraian Sea and sailed through the Southern Sea; and when autumn came, they would put to shore and sow the land, wherever in Libya they might happen to be as they sailed, and then they waited for the harvest: and having reaped the corn they would sail on, so that after two years had elapsed, in the third year they turned through the Pillars of Heracles and arrived again in Egypt. And they reported a thing which I cannot believe, but another man may, namely that in sailing round Libya they had the sun on their right hand.
[...] Sataspes [...went] into the presence of king Xerxes, he reported saying that at the furthest point which he reached he was sailing by dwarfish people, who used clothing made from the palm-tree, and who, whenever they came to land with their ship, left their towns and fled away to the mountains: and they, he said, did no injury when they entered into the towns, but took food from them only. And the cause, he said, why he had not completely sailed round Libya was that the ship could not advance any further but stuck fast.
(My emphasis) These facts, far from being "fantastic", are all very likely. In particular the last one has been confirmed only relatively recently, when it was discovered that Pygyes used to inhabit coastal areas of Equatorial Africa before the expansion of the Bantu. The "thing [he] cannot believe" is very hard to explain without admitting that Phoenician travelers had passed the Equator and that the episode was popular enough to reach Herodotus and for him to recount it. We had to admit that ancient seafarer peoples had much more extended knowledge about the world than we were previously convinced of.
Back to the question, if we intend lost only as physically inaccessible, then many archeological findings can be classified as "thought to be lost" and later rediscovered.
- A: Just because I'm lazy I'd cite again the discovery of the royal archives in Hattusa.
- B: the discovery of Pompei was much more important, in that it brought a wealth of information about life in the Roman Empire.
- C: a somewhat small discovery as the serendipitous finding of a room of Domus Aurea left a trace in modern language in the word grotesque and allegedly had some role in the Italian Renaissance, with the greatest artist visiting the room before the frescos vanished.
If we instead strictly limit ourselves to documents thought as written documents only, I would like to cite:
- A: The discovery of the Tocharian civilization in Central Asia, near the border of the Tarim Basin, had profound implications for Indoeuropean studies. It shifted eastward by several thousands miles the baricenter of the Indoeuropean people.
- B: Hattusa's royal archives contain extended historical records. These, unlike e.g. contemporary Egyptian records, are considered much more reliable. In fact, because of their religious convinctions, Hittite Kings were not allowed to distort the facts too much, whereas the Pharaohs used to record events mostly for propaganda reasons 
The best known example is the recording of the Battle of Kadesh, which was reported as a crushing victory in Egyptian records. Reality was probably different, if the Egyptian sphere of influence stayed roughly the same. The following peace treaty is the first international treaty, and a copy of it is displayed in New York in the UN Headquarters.
- C: dulcis in fundo, and perhaps my best answer to your question, also in terms of impact, is the rediscovery of the classical heritage during the first phase of the Renaissance. A considerable part of classical culture was temporarily lost, and only preserved thanks to monasteries. It was there that the great scholars of the period re-discovered lost and forgotten works, leading to a great change in perspective and knowledge culminating in the Renaissance proper.
This list is necessarily incomplete, because of the subjective nature of the "impact" a discovery has. Even though my preference goes to the last item, then there is no specific document I would pick as the most important one. Consider However that we are speaking about rediscovery of Cicero and Livy, among others. Think about such a discovery nowadays...
PS. The Jordanian Lead Codices are almost certainly a forgery. I had heard of the discovery in 2011 but did not investigate further developements until the time of writing this answer.
: Hetiter. Die unbekannte Weltmacht, B. Brandau & H. Schickert, Piper Verlag GmbH, Munich, 2001