The precise reasons behind the board’s unwillingness to negotiate with Mr. Lee aren’t entirely clear, but his sudden departure without a successor in place has had the effect of exacerbating one of the firm’s perennial problems: the underperformance of its stock price.

Shares of Carlyle fell more than 6% Monday to close at $35.29.

The surprise announcement late Sunday night, which came after The Wall Street Journal began inquiring about the matter, is a rare instance in which a handpicked successor to a private-equity firm’s founders has been shown the door.

When Mr. Lee took the helm of Carlyle, its shares had consistently underperformed peers’ and the broader market since its 2012 initial public offering. This was in large part because it was slow to launch businesses that generate the steady, predictable management fees prized by shareholders, such as credit and insurance, remaining too concentrated on the volatile private-equity business.

The growth in Carlyle’s assets under management also lagged behind peers. At the end of 2012, Carlyle managed about $170 billion, roughly 80% of

Blackstone Inc.’s

total and significantly more than that of

Apollo Global Management Inc.

or

KKR

& Co. By the time Mr. Lee became CEO, Carlyle’s assets were 45% of Blackstone’s and 78% of Apollo’s. KKR would soon surpass it too.

Mr. Lee’s job was to simplify and modernize the business and take it in new directions. That required jettisoning some of Carlyle’s subscale businesses and consolidating others. He also tried to make changes to the firm’s culture, pushing its investment professionals to be more collaborative, and focused his efforts on growing fee-generating businesses.

A seasoned investor, Mr. Lee had good instincts when it came to getting Carlyle on stronger financial footing: The firm’s shares continued to underperform those of its peers, but Mr. Lee succeeded in closing the gap significantly, with Carlyle shares, including dividends, outperforming the S&P 500 during his tenure.

In the second quarter, assets under management for Carlyle’s credit segment nearly doubled year-over-year to $143 billion, surpassing the firm’s private-equity segment for the first time. Fee-related earnings climbed 65% to $236 million.

He got paid handsomely for his services. He made $42.3 million in 2021, according to a securities filing. While that may sound steep, it isn’t very high by private-equity standards. Blackstone CEO

Stephen Schwarzman

made $160.3 million that year. KKR reported paying co-CEOs

Joseph Bae

and

Scott Nuttall

compensation valued at $559.6 million and $523.1 million, respectively.

Still, the host of changes he rolled out often didn’t endear him to his colleagues, and a number of long-serving investment professionals left the firm.

The board now wants someone with a track record as the leader of a global company to continue to execute the strategy, according to a person familiar with its search criteria.

Some investors and analysts questioned the abrupt change Monday.

“While Conway is a capable leader and well known to investors, this news will likely drive some investors to question Carlyle’s ability to truly transform into a more collaborative and balanced business mix, which will be key to its valuation catching up with comps,” Autonomous analyst Patrick Davitt wrote in a research note Monday.

The fact that the firm appears to be searching outside for a successor suggests it has a less seasoned bench than many of its competitors, he wrote.

Write to Miriam Gottfried at Miriam.Gottfried@wsj.com