Lima made his international debut for Western Samoa in 1990 and has built a fearsome reputation for his ferocious work in defence, earning the nickname "the chiropractor".
The 33-year-old, who has signed a two-year deal with Bristol, featured in the famous World Cup win over Wales in 1991 and was last employed by Munster.
Lemi, 22, has been the IRB World Sevens Series' top scorer over the past two seasons and is Samoa's sevens captain. He has agreed a one-year contract.
"Brian Lima will bring international experience to our backline," Bristol's head coach Richard Hill said. "He will also be a massive physical presence. David Lemi is less well known but he is a very exciting talent. He's been a star of the World Sevens Series in the past couple of years and has been a prolific try scorer. We've captured the best in Samoan backline talent with the class of Lima and the potential of Lemi."
Elsewhere, the South Africa coach, Jake White, has dropped three players from his squad for the second Nelson Mandela Challenge match against Australia. The utility back Brent Russell, prop Lawrence Sephaka and flanker Danie Rossouw make way after playing in Saturday's 30-12 defeat in Sydney.
The 23 July game at Ellis Park Stadium is White's last chance to view players before the start of the Springboks' Tri-Nations title defence. The prop Eddie Andrews was recalled, together with flanker Solly Tyibilika, an unexpected omission from the Australian trip.Reuse content