Such acts will not be tolerated "no matter what social status or political background, or political views (of any individual)," Secretary for Justice Rimsky Yuen told reporters.
He said police will investigate the firebombing like any other criminal act.
Some feel that Hong Kong police don't always follow up fully on acts against the city's democrats or against Apple Daily, and that culprits are rarely found.
Hong Kong police confirmed they were looking into two incidents, one at a residence on Kadoorie Avenue in Kowloon and one at the offices of Next Media.
Lai, who stepped down as chairman of Next Media and as publisher of the Apple Daily tabloid in December, is a well-known critic of Beijing.
He was arrested for refusing to leave a pro-democracy protest site in central Hong Kong last month as police cleared protesters who had shut major thoroughfares in the city for two-and-a-half months.
A self-made millionaire, Lai is a long-time supporter of Hong Kong's democracy movement. This is not the first time he and Next have come under attack.
In 2013, masked men torched tens of thousands of copies of two Apple Daily editions at distribution points.
Last year, Next said HSBC Holdings and Standard Chartered pulled millions of dollars worth of advertising from Apple Daily after being pressured by Beijing, decisions both banks said were commercial.
Lai's home has also been attacked before, including being rammed by a car and having a machete, ax, and threatening messages left in his driveway.
He remains the majority shareholder in Next Media, which publishes Next Magazine and the Apple Daily.