What is the purpose of this unreachable lever?

Solution 1:

That elevator goes to Blackreach. You will go there as part of the main quest. There are quite a few of them scattered throughout the land. Once you enter Blackreach, you will open the gates from the inside.

Lift locations:

• Great Lift at Alftand
• Great Lift at Mzinchaleft
• Great Lift at Raldbthar

Solution 2:

It's a "Great Lift" (i.e. elevator) coming from a vast underground Dwemer ruin. They all connect to a place called Blackreach which you run into during the main quest line.

There are three great lifts that come up from the ruin and you can get down (and up) via four other locations: Alftand, Mzinchaleft, Raldbthar and the Tower of Mzark. The Blackreach page on UESP has more detail about the quest itself and locations where you can travel down to the ruin.