So, I make my way through Balckreach to the Tower of Mzark. However, all the buttons are locked and the Elder Scroll is already displayed. I take the Elder Scroll, but the quest does not advance and it does not show in my inventory. Also, I cannot get the blank lexicon in the lexicon holder next to the buttons. Have I screwed something up? Any workaround?

If you have never entered Mzark with this character before, then you have a serious problem.
If you have done Discerning The Transmundane and recived the Oghma Infinium, you can try dropping the Elder Scroll, then picking it back up to further the questline for Elder Knowledge.

I had to use console command to finish the quest, so, in the end, NBD.