Mr Lazarus said he was very pleased to lead the party in the Senate.
He said he looked forward to working with the other Palmer party senators and Australian Motoring Enthusiast Party senator-elect Ricky Muir, who has agreed to vote as a bloc with the Palmer party.
Party founder Clive Palmer announced Mr Lazarus' new role, saying he'd be a firm leader for the party.
Mr Palmer said his own place in parliament was still not assured, with a full recount underway in the Sunshine Coast seat of Fairfax.
There was no word on any move by Mr Muir to defect to the Palmer party.
Mr Palmer has previously played down the prospect, despite a meeting scheduled for Wednesday about Mr Muir's future with the motoring party.
The party's Victorian branch has claimed it wasn't properly consulted about Mr Muir's deal to vote with the Palmer party.
Mr Lazarus told reporters he'd not yet had a chance to look at the federal government's carbon tax repeal bill.
"I've dedicated my time to my wife and family over the last couple of weeks. I don't start my role until July next year. That's when it'll be a main issue for me," he said.
Mr Palmer said he wouldn't undermine the current Senate's position by talking about what stance his party would take on conditions applied to the carbon tax repeal.
He said Prime Minister Tony Abbott had put the onus on the Labor party to agree to repeal the tax in the term of the current Senate.
Mr Palmer said the national executive of the motoring party last week expelled members who were due to meet on Wednesday to consider Mr Muir's future.
"These people are no longer members of the Australian Motorists Party. It makes no difference what they do," he said.
"Ricky Muir is elected as a senator from Victoria.
"People who are expelled from a political party don't have any authority or rights to remove anyone from the senate."
Mr Palmer dismissed any suggestion his party's senators could vote according to his business interests.
Such suggestions were "bulls***", he said.
"Well just hold on for a minute," Mr Palmer said as Mr Lazarus was responding to a question about the impact of the miner's business interests on policy.
"If I have an interest I will declare it. It's not about parties having conflicts of interest.
"It's a load of bulls***.
"Glenn doesn't have a conflict because he's a member of our party. That's just a load of rubbish really."
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