Former Fiji under-20 player Tavatavanawai, who made his test debut during the France series in July, fractured a radius bone playing for Tasman in domestic rugby and will be out for an estimated 12 weeks, New Zealand Rugby (NZR) said on Monday.
Lienert-Brown missed New Zealand's first-ever defeat to the Pumas in Argentina following a head-on-head clash in the opening test in Cordoba for which he earned a yellow card.
He returns after completing concussion protocols.
Experienced prop Lomax will be available for selection for Saturday's clash at Eden Park in another boost for the All Blacks after missing the Argentina tests with a hand fracture.
Scott Robertson's New Zealand lead the Rugby Championship on six points after the opening two tests, one ahead of second-placed Australia.
South Africa are third on the table with four points following their 30-22 win over Australia in Cape Town.
Cortez Ratima is being monitored after sustaining a rib fracture in Buenos Aires, NZR said, while fellow scrumhalves Cam Roigard and Noah Hotham are unavailable for both home tests against the world champion Springboks at Eden Park and Wellington.
Waikato Chiefs halfback Xavier Roe has been brought into the Auckland camp as injury cover for Ratima.
Winger Caleb Clarke and loose forward Luke Jacobson have recovered from respective ankle and thigh injuries but will be rested from the Eden Park test and look to return for the following week's clash in Wellington, NZR said.
With lock Patrick Tuipulotu sidelined with a facial fracture, Sam Darry comes into the squad as injury cover