One possible solution:
To reset the puzzle, use the ESC key to pull back and then open the door again.
Highlight the outer ring of the left oval.
Use the enter key until the middle left oval and the outer left oval form UM somewhere around the oval and out of the bars.
Use the left arrow key to highlight the middle left oval.
Use the enter key and note that UM now rotates at same speed but the innermost turns at different speed.
Now use the enter key to turn and form LUM somewhere around the oval.
Use the left arrow key to highlight the innermost left oval.
Use enter key to see that the left oval's rings turn still forming LUM and place it between the bars. It should show LUMEW as of now.
Highlight the inner ring of the right oval. Turn it to get N to match the LUME that should be within the bars.