The giant golden globe roughly in the centre of Blackreach is not the lexicon machine, but it provides a useful point of reference to find it. While standing below the giant golden globe, walk directly south. As you pass through the southern gate of the wall, you will be on top of a set of stairs. Slightly to your right is a tall tower that connects to the ceiling. This is the Tower of Mzark. To reach it, you will cross a bridge over rapids which flow to the edge of a waterfall. When you reach the tower, take the elevator to the tower's interior, solve the puzzle, and you will be able to transcribe the Elder Scroll into the lexicon and then retrieve the Elder Scroll from the machine.
When your follower "dies", they enter a pre-death state that generally allows them to come back to full health immediately after battle. However, if they continue to take more damage after entering that state, they will die permanently.
If there's a chance your follower is still alive but nowhere to be seen (for example, if they entered the pre-death state and you ran off, thinking they were dead dead), fast traveling to a location should cause the follower to appear back at your side.
If fast traveling still doesn't produce your follower, they're almost certainly fully dead. You can confirm this by trying to pick up another follower: if they agree to come with you, the other follower has ceased to be. Sorry about that.
The only thing you can do at this point—if you're not keen on loading up an earlier save or using console commands—is to find where your follower died and loot their corpse.
If you are amenable to using the console, generally you still need to find where your follower died to ressurrect them: when you do, open the console, target their corpse, and type:
resurrect 1
and press enter.
However, you can get around even this restriction by selecting the follower by using the prid command anywhere:
prid <RefId>
Where <RefId> is the ID corresponding to the follower, found by using the Creation Kit or by looking up the follower on UESP. Once the follower's selected, use the resurrect command mentioned above.
Best Answer
There is no use for the Runed Lexicon after the quest is complete. It is supposed to disappear after the quest is complete but there is a bug which may mean it does now, If you loot it from Septus' corpse, you may not be able to drop it. If you are playing on the PC, you can get rid of it with the following console command:
If you're on a console, there's no known fix for the bug.