In the 1980s, Ludmila Zaitseva was a participant of the multiple USSR Women's Chess Championship finals. Two times she won the Soviet Team Chess Championship: in 1983, with the Moscow city team, and in 1985 as a member of the Russian SFSR team. In 1987, Ludmila Zaitseva participated in the Women's World Chess Championship Interzonal Tournament in Zheleznovodsk where shared 3rd-4th place with Agnieszka Brustman. An additional match between the two chess players ended in a draw - 3:3, and thanks to better Berger score in the main tournament Brustmane entered in the 1986 Women's Candidates Tournament. In 1995, Ludmila Zaitseva second time participated in the Women's World Chess Championship Interzonal Tournament in Chișinău where shared 32nd-38th place. Ludmila Zaitseva two times won Russian Women's Chess Championship: in 1993, and in 1996. In 1996, she won Ludmila Rudenko memorial chess tournament in Saint Petersburg. In 1998, Ludmila Zaitseva reached the Russian Women's Chess Cup semi-final in which she lost Svetlana Prudnikova, and also she lost Alisa Galliamova in the match for the 3rd place. In 2003, Ludmila Zaitseva shared first place in the Women's Chess tournament dedicated to the 300th anniversary of the foundation of St. Petersburg.