I've searched a bit the forums for the subject I'm about to bring up, I don't think it was already discussed, all I can remember are a few occurences were some other forum users seemed to go in the same direction.
One thing that is amazing with procedural generation is this quality : it makes the environments look as if they were preexisting, not man-made, and that is the true beauty of a game that is going to be set in space : Josh sets the rules but let the magic happen by itself - and by the power of maths.
So, in my mind, that situation were anything can happen, were no one knows in advance what the next system will look like, is one of the things that makes the game feel really epic.
I'm going to quickly digress and mentions other games that, at first sight, have barely anything to do with LT :
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If some of you are familiar with Ico and Shadow of the Colossus ( I know, this is a long shot, humor me, you'll see where I'm going ), they might remember the "Secret Garden".
I'll quickly try to explain for those that don't know : in Shadow of the Colossus, at the center of the map, was a huge temple. Some time after the release of the game, people noticed that there seemed to be a path that allowed to climb it. People started imagining all sorts of things, from a secret ending to a hidden character/boss...
Then, the mystery behind this place was finally solved, but people kept thinking there was always more hidden somewhere in the world. At some point, someone found an immense dam that had been cut from the game... but also let there, hidden somewhere in the map. These stuff fed the imagination of players even further, and I'm sure those who still play this game keep feeling this voice in the back of their head.
"There's more to this, somewhere."
Another example want to mention, before I eventually attempt to make my point, is the Dark Souls Lore : for those who don't know it, or those who know it but aren't interested in it, it is one of the most captivating lore I've seen in games, mostly because it breaks a lot of preestablished rules we've had in fantasy - and games in general. It also had the player put in the position where he has to figure out things by himself, only being given clues here and there - heck, not even being given those clues, you had to dig them up yourself.
If you can remember how you felt when you first reached Ash Lake, or when you found that huge skull in there and wondered what creature that could have been, you'll know what I'm pointing out.
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"Where the hell is he going with all this "lore" gibberish ? LT will have no storyline, no lore..."
I know, I know.
Knowing these examples, you'll understand me better when I say that I want the unexpectedness that lies within a procedurally-generated world to be pushed even further... I'd like sometimes to have my ship systems to stop working for a second, to have my scanner pick unknown signatures for a few seconds, to have the system map simply not working in some systems ? There are lots of things we don't understand in the universe, physical phenomenons do sometimes occur for reasons that are yet unknown due to our limited knowledge of the universe.
I'd also like the algorithms to allow some empty systems to be generated. It is the abyss, the unknown, the darkness, the void, the cold that makes space what it represents in our imagination, and I hope these qualities make it to the game.
There has to be unnamed planets, sterile ones, unuseful ones, empty systems, maybe, who knows, shipwrecks ?
The final word is for Josh : keep up the good work. And, you know, you can have your little secrets. Maybe you have to. Go nuts, put some mystery in there, you don't have to tell us everything !

Thanks for reading me !
Notes :
- I'm not creating this thread in the "suggestion" section on purpose, because the goal is to discuss this with other users more than really suggesting features to be implemented.
- Here's a link towards an article that deals with the state of mind the Shadow of the Colossus put the players in, hopefully that helps understanding me and my point better :
http://www.eurogamer.net/articles/2013- ... big-secret