Bacall's cause of death has not been released by her family. Here's the official announcement in regards to her death:
https://www.facebook.com/HumphreyBogartEstate/photos/a.656550261051...
Exact words:
"With deep sorrow for the magnitude of our loss, yet with great gratitude for her amazing life, we confirm the passing of Lauren Bacall."
The media speculated it was a stroke because medics were called to The Dakota in the morning (Bacall died in the afternoon) for someone in the building suffering stroke like symptoms-that person was taken to the hospital, while Bacall died at home.
Therefore, the bottom line is that the stroke victim at the Dakota that day was not Bacall and the cause of death has not been released.
http://www.cnn.com/2014/08/12/showbiz/lauren-bacall-dead
According to her grandson via CNN:
Bacall's grandson said he got a call early Tuesday from his father.
"She apparently had a stroke. A pretty massive stroke. That's what happened," said Jamie Bogart, who last saw Bacall over the holidays.