Hedge fund TCI led an unsuccessful campaign to oust LSE Chairman Donald Brydon last year over his handling of the departure of long-standing group CEO Xavier Rolet.
After the LSE named Goldman Sachs' veteran David Schwimmer as its new CEO earlier this month, a source close to TCI told Reuters on Tuesday the hedge fund appeared to back the new appointment.
He said a meeting had been arranged between Schwimmer and TCI, but it was not clear if it had taken place.
The LSE also said a review of how it handled Rolet's departure found its board did not act improperly, but recommended some improvements for the future, including a greater engagement between the board and shareholders.
"The things they are suggesting they will do are all good and proper things to have," said the source close to TCI. "We still think it's a good company."
The LSE said total income from continuing operations rose 13 percent to 520 million pounds in the quarter ended March 31, with total revenue up 11 percent at 470 million pounds. Growth was driven by its clearing, capital markets and FTSE Russell indexes businesses.
Schwimmer's first challenges, after he takes the helm in August, will include helping the 300-year-old LSE to navigate Britain's departure from the European Union, and leading its efforts to woo oil giant Saudi Aramco <IPO-ARMO.SE> for what is expected to be the world's largest initial public offering.
In particular, he will have to protect the LSE's stronghold in clearing euro transactions, as rival Deutsche Boerse in Frankfurt seeks to exploit uncertainty over Brexit to snatch market share.
RBC analysts said the LSE was equipped for the battle.
"The LSE would have more than 900 million pounds in balance sheet capacity for M&A or further returns to shareholders," they said. RBC has an "outperform" rating on LSE shares, which were up 0.5 percent to 42.38 pounds at 1035 GMT.
Last year, European Union regulators blocked a 29 billion euro (25.4 billion pounds) merger between the LSE and Deutsche Boerse, formally ending a deal that unravelled in the wake of the Brexit decision.
The LSE itself is widely viewed as a potential takeover target, with rivals Intercontinental Exchange and CME in the United States long seen as suitors.
CME agreed to buy NEX Group for $5.5 billion (3.95 billion pounds) last month, creating a cross-border powerhouse for investors trading in the multi-trillion dollar foreign exchange and government debt markets.
Analysts say the tie-up will allow the U.S. exchange operator to challenge the LSE's dominance in the over-the-counter clearing market.
(Reporting by Noor Zainab Hussain in Bengaluru; Additional reporting by Maiya Keidan in London; Editing by Carolyn Cohn and Mark Potter)
By Noor Zainab Hussain