Lawson, 49, last month succeeded former England batsman Woolmer, who died during the World Cup in the Caribbean five months ago. He edged out two other short-listed Australians, Dav Whatmore and Richard Done.
A former Australian Test fast bowler, he said he could not see a downside to what is arguably the most volatile job in international cricket.
For every congratulatory message Lawson has received since his appointment, he said friends have bombarded him with references to stranglings, suicide bombings, flaming effigies and the whereabouts of Osama bin Laden.
Yet Lawson, who leaves for Lahore on August 21, denies having any doubts about his new role.
He said he had already decided to accept the two-year post when he received a letter from Woolmer's widow, Gill, who lives in South Africa.
"It's a lovely letter about how he loved coaching Pakistan, loved the people and she wished me all the best," Lawson told a Sydney newspaper.
"It comforted me in the fact (Woolmer's family) gave me their support and they don't have any concerns whatsoever."
A bungled investigation into Woolmer's death at this year's World Cup began as a murder case but concluded, months later, that he died of natural causes.
There are wider security issues in Pakistan. The Australian field hockey team has withdrawn from the Champions Trophy in Lahore in December following last month's bloody military siege at the Red Mosque in Islamabad.
A Cricket Australia delegation has returned from a security mission to Pakistan, confident Australia's first tour of the country in 10 years will proceed next March.
Lawson said he was shocked by what he described as an extraordinary misunderstanding of safety in Pakistan.
"The amount of people who have said to me congratulations, but you're mad," Lawson told the newspaper.
"There are less concerns than I'd have going to London or New York. I was in England in 2005 when all the bombs went off, and that was scary.
"(People) see the Red Mosque shootout there and hear about bin Laden hiding in the hills of Pakistan. But it's like if you're hiding in outback Australia and you live in Sydney.
"The Australian hockey team decided not to go, I find that astonishing. As sports people in Australia are revered, sports people in the sub-continent are deities almost. If you're involved in sport, that's the safest situation to be in."
The Pakistan board has demanded a major tournament victory in the next two years, a condition which Lawson deems to be fair.
"I don't have fears of failure, I don't have fears of outside influences, I don't have fears of dealing with politics," he said.
"For me, it's an adventure as well. You don't live there that much and I think that's a bit of a pity. I'd love to live for three months with the people."
Lawson's family will remain in Sydney, which he says is a practical solution for his son, who will begin senior high school next year.