Lee pipped Russia’s Angelina Melnikova and Brazil’s Rebeca Andrade.
Despite a fall on the beam, the 16-year-old scored 53.965 to eclipse Team GB’s previous best of 12th by Becky Downie in Beijing in 2008.
The tourists will be looking to claim an unassailable 2-0 lead in the series in Cape Town this weekend.
British & Irish Lions captain Alun Wyn Jones expects wounded South Africa to put more emphasis on the set-piece in the second test as they try to wrestle control in the game and level the three-match series in Cape Town. The Springboks started the better in the opening match of the series and led 12-3 at halftime, but the Lions clawed their way back into the contest with scrum domination and an accurate kicking game that proved decisive in the final 22-17 scoreline. Jones believes the Boks will come flying out the blocks, and says the set-piece, especially with the hosts' 6-2 split on the bench between forwards and backs, means they are likely to focus heavily on what has traditionally been the strength of the team.