Rizwan and Irfan both suffered hamstring injuries in the third match in Rawalpindi, where a second-string New Zealand side won by seven wickets to level the five-match series 1-1
The left-hander dropped his bat and slumped to his knees after an attempted hook shot went awry at Marrara Oval in Darwin on Tuesday, but quickly picked himself up and walked off the ground unassisted.
With the squad set to depart for Bangladesh on Friday ahead of the first Test in Dhaka, which starts on Aug. 27, Lehmann expected Warner to board the flight.
"He seems alright, walking around the ground today, so fingers crossed he'll be okay and we'll get an update in the next day or two," Lehmann told reporters.
"It's always a scare when that happens, isn't it? Hopefully he's going to be OK."