The two deaths occurred within one week, the local health ministry said.
The victims were a couple, aged 56 and 35 respectively.
The couple had just returned from the burial of their grandchild who had a brief illness in Bong County, also in central Liberia.
Laboratory tests conducted on the blood specimen of the two victims confirmed that they died between May 4 and 7, with the husband first giving up the ghost, the health ministry said.
Margibi county health officer Myer Pajibo told a news conference that 60 persons are being monitored as close contacts of the victims.
At least 14 people have died of Lassa fever in Liberia since the beginning of the year. At least 30 cases of the viral hemorrhagic fever caused by the Lassa virus have been recorded in the west African country since January.
Only four counties have been affected by Lassa fever in Liberia, which has a total of 15 counties.
Humans usually become infected with the Lassa virus from exposure to urine or feces of infected mastomys rats. Other than common preventive measures such as washing hands regularly, the World Health Organization has recommended keeping cats.