Weintz said Monday that Fallin reached Lane's father over the weekend and personally offered her condolences.
Wallace drew parallels between the Lane killing and that of Florida teen Trayvon Martin, saying Obama had spoken out “quite quickly” about Martin's death.
Two of those alleged to have killed Lane are black; Lane was white. In the Florida case, Martin was black; George Zimmerman, who was acquitted of charges connected to Martin's killing, is Hispanic.
Fallin declined to engage in a discussion about race in connection to the case.
Fallin also rejected the idea that the killing was connected to the “easy availability of guns” in Oklahoma.
“Well I don't think this issue is about gun control,” she told Wallace. “It's an issue about murder. It's an issue about three young men who did something very terrible to a very innocent bystander that was jogging through his community, and it's very unfortunate what has happened.
“And I certainly understand that Australia is very upset. People in Oklahoma are very upset too; people in the United States are very upset with what's happened, because it's just such a shock that anyone would do what they had done to Chris Lane.”