It became the biggest private equity firm of all by venturing beyond its buyout roots.
Over the past decade, Athene has grown into the firm's biggest profit driver and the largest annuities provider in the U.S.
Investors asked to redeem $4.5 billion in April from Blackstone Real Estate Income Trust.
The real estate industry has come under pressure as investors seek to reduce their exposure.
Lee's death has ushered in a new level of public attention for a shop that manages $3 billion.
Schwarzman, who owns some 20% of Blackstone shares, reaped about $1 billion in dividends.
Lee reportedly died in his office on Thursday of a self-inflicted gunshot wound.
Schwartz will take the reins of a firm that has grappled with management turnover.
The firm's crown jewel continues to wrestle with investors seeking to get money out.
Blackstone's ambitions for a record-breaking buyout fund have crashed into reality.