If the third person is infected, Lumsden could be charged with wounding with intent to cause grievous bodily harm.
The alleged offending was revealed after one man told his GP about the sexual encounter.
The doctor felt he was obliged to tell him that Lumsden was HIV-positive, Detective Senior Sergeant Scott Anderson said.
Police now want to speak to anyone else who may have had unprotected sex with Lumsden.
Some former partners have already been spoken to, Anderson said.
"Some didn't fall into the category of unprotected sex, some already had the HIV virus, and a number of others didn't want to engage with the police," Anderson said.
He said the men should have a sexual health check and then see police "if they would like to pursue it any further".
Although police are focusing on encounters in Canterbury, more partners could come forward as Lumsden had lived in Australia. He was originally from Northland, Anderson said.