New Zealand-born flanker Lam, a former Australian schoolboy international, and specialist centre Leiua both play for the Wellington Hurricanes.
Scrumhalf Auvasa Faleali'i, recently signed by Australia's Waratahs, is also among the newcomers in a 31-man squad selected by coach Stephen Betham released in a statement passed on by the South African Rugby Union.
Hooker Manu Leiataua from North Harbour in New Zealand's domestic competition, Japan-based centre Brandon Va'aulu and Isaia Tuiua, a centre with Spanish club Vigo, are the other uncapped players.
Winger David Lemi, who captained Samoa when they beat Wales in Cardiff in November, was not named in the squad but two more players are still to be added.
Samoa face the Lions in Johannesburg on June 1, followed by tests against Scotland in Durban on June 8 and Italy in Nelspruit on June 15. They will play a further test in Pretoria on June 22 against one of South Africa, Italy or Scotland.