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The first thing that came to mind was the Rosetta Stone. While King Ptolemy V Epiphanes' decree that's inscribed in it is not particularly significant, the Rosseta Stone is a trilingual inscription, written in hieroglyphics, demotic Egyptian and Greek, and it's discovery in 1799 lead to the decipherment of hieroglyphics and thus to a far better understanding of Ancient Egypt. The Rosseta Stone was discovered during Napoleon's campaign in Egypt, and it has a bit of a turbulent history that hasn't settled yet. Almost every multi-lingual inscription discovered was similarly significant, another example would be the Pyrgi Tablets that were key in deciphering the Etruscan language.
Moving on to a more traditional document, Corpus Juris Civilis, the Code of Justinian, was probably accidentally re-discovered in 1070 in northern Italy. It inspired the Napoleonic Code (1804) that abolished feudalism and is often quoted as the root of western legal traditions.
Upvote:13
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.
[...] 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.
If we instead strictly limit ourselves to documents thought as written documents only, I would like to cite:
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.
[3]: Hetiter. Die unbekannte Weltmacht, B. Brandau & H. Schickert, Piper Verlag GmbH, Munich, 2001