The former Australian fast bowler is at home in Sydney with his family and is scheduled to return to Pakistan in the next two weeks.
Lawson could not say what impact the death of Bhutto, who was killed Thursday in a gun and bomb attack in the northern city of Rawalpindi, would have on his own future with Pakistan cricket.
Lawson is five months into his two-year contract with the Pakistan Cricket Board and has a get-out clause in his deal if he decides not to return.
His family has remained in Australia during his stay in Pakistan, where he is based in Lahore.
"I'm making informal investigations with people I know in Pakistan to get their opinions," Lawson said here.
"I've sent a few emails this morning just to people I know in Pakistan in different areas to get their opinions.
"I'm very open (to what they say) and I'm more likely to take into account what they've got to say rather than any officials. I'm just seeking advice, I'm not pre-judging anything."
Anger over Bhutto's death has triggered violence that has left at least 10 people dead.
The unrest across the country has also cast doubt on Australia's scheduled cricket tour there in March.
Lawson was appointed Pakistan coach in July after the death of Bob Woolmer during the World Cup in the Caribbean.