"We see this as straight harassment," the source said, adding that Lai was arrested on suspicion of sedition, criminal fraud and colluding with foreign forces.
Hong Kong Journalists Association chairman Chris Yeung said the search was "horrible".
"I think somewhere in third-world countries there has been such kind of press freedom suppression; I just didn't expect it in Hong Kong."
Taiwan Premier Su Tseng-chang said "China should not treat Hong Kong this way."
On major cases in Hong Kong, the central government in Beijing can claim jurisdiction. The legislation allows agents to take suspects across the border for trials in Communist Party-controlled courts.
Apple Daily executive Chan Pui-man said the newspaper will be published on Tuesday.
"Even if Apple Daily publish a pile of blank paper tomorrow, we would go and buy a copy," prominent young activist Joshua Wong said on Twitter.
Not intimidated
Jimmy Lai was also arrested this year on illegal assembly charges, along with other leading activists, relating to protests last year.
In a Reuters interview in May, Lai pledged to stay in Hong Kong and continue to fight for democracy.