* HK leader sends condolences to Liu Xiaobo's wife and family
* HK leader Lam pledges to defend city's core interests
* Lam says city needs stronger leadership in financial sector
* National security laws to be enacted "as soon as possible"
* Lam acknowledges concerns over individual incidents (Updates to add exclusive tag)
HONG KONG, July 14 (Reuters) - Hong Kong Chief Executive Carrie Lam said on Friday she shares the compassion of people over the death of Chinese dissident Liu Xiaobo and acknowledged "anxieties" about "incidents" in the former British colony that can potentially erode its autonomy.
Lam was speaking in her first interview with the international media since she was sworn in as the city's new leader by Chinese President Xi Jinping on July 1.
"Hong Kong people are always very compassionate and so I share that compassion of many Hong Kong people by sending my condolences to the wife and the family of Mr Liu," Lam, a devout Catholic, told a Reuters Newsmaker event in Hong Kong.
Chinese officials have long branded Liu as a "subversive" so such comments are unusual and the only sympathetic remarks so far from a Beijing-backed leader regarding his death.
Liu, who won the Nobel Peace Prize in 2010 for his efforts to promote democracy in China, died on Thursday at the age of 61 of multiple organ failure while in detention.
Liu was jailed for 11 years in 2009 for "inciting subversion of state power."
Hong Kong, a former British colony, returned to Chinese rule in 1997. It enjoys wide-ranging freedoms not granted in mainland China, a promise of full democracy at some future date, and an independent judiciary under a so-called "one country, two systems" formula.
But the abduction by mainland agents of Hong Kong booksellers who had published critical books on China, and Beijing's efforts to disqualify democratically elected, pro-independence lawmakers in the local legislature, have rattled confidence in that arrangement.
'ANXIETIES AND PERCEPTION'
In a wide-ranging interview, Lam acknowledged concerns about certain "individual incidents" in the city. She said it was her duty to accurately reflect them to the central government in Beijing.
"I would say there are worries, there are anxieties, there is a strong perception over individual isolated incidents, but unless you've got evidence to prove there are clear breaches then it will remain at the level of anxieties and perception," Lam said, without elaborating.
She did say, however, police were still investigating the booksellers' cases.
Britain called the cases a "serious breach" of the Joint Declaration -- the 1984 treaty that paved the way for Hong Kong's return to China -- and said one of the booksellers, a British passport holder, had been removed from Hong Kong "under duress."
Hong Kong's high court on Friday removed four opposition lawmakers from the city's legislative council for failing to sincerely take the oath of office, in a significant blow to the opposition that could weaken its one-third veto bloc in the 70-seat assembly.
While the lawsuit had been initiated by her predecessor, Lam said she wouldn't intervene in the case
"Building bridges still has to be done in a lawful way. I dont think this CE (chief executive) or any government official should compromise on the rule of law just because we want to be friendly. But Im sure the judicial process will go on."
Speaking about Hong Kong's financial sector, Lam said it has a lot of catching up to do, particularly given big strides in financial technology on the mainland, and needs stronger leadership. She also expressed concern over stock price manipulation in the territory.
XI'S HARDER LINE
Xi took what some saw as an explicitly harder line about Hong Kong's future during his visit marking the 20th anniversary of the financial hub's return from British to Chinese rule.
Xi warned in a speech that any attempt to endanger Chinese sovereignty and security, challenge its power, or use Hong Kong to carry out infiltration and sabotage activities would be acts that cross "the red line" and are "absolutely impermissible."
Lam said she would seek to enact contentious national security laws, known as Article 23, "as soon as possible," without giving a specific timetable, that would prohibit acts of treason, secession, sedition and subversion against China.
A proposed blueprint for those laws in 2003, however, was seen as a grave threat to Hong Kong's autonomy, and drew a half-million protesters to the streets before it was finally shelved.
Over the past two decades, Hong Kong's "one country, two systems arrangement" has come under considerable strain, as the city's opposition forces have agitated for full democracy and railed against creeping Chinese interference in various sectors including business, politics, media, law and education.
The 60-year-old Lam has said she hopes to lead Hong Kong "towards new glory" in the next five years and heal divisions that have festered since the massive 2014 pro-democracy protests that blocked major roads in Hong Kong for 79 days.
Lam also pledged to stand by the people of Hong Kong in protecting their rights.
"If our core values are being undermined by whatever things happened both in Hong Kong or not in Hong Kong, then of course I have that duty."
At times, Lam, the mother of two grown sons, showed a lighter side, boasting that she slept soundly through the night when asked about the insomnia of leadership.
She expressed hopes she could ease the pressures of Hong Kong's pressure cooker school system, saying parents should let their children "dream" - and acknowledging that was not a traditional Asian "Tiger Mum" thing to say.
(Additional reporting by Anne Marie Roantree, Venus Wu, Twinnie Siu, Greg Torode. Editing by Bill Tarrant)