As a junior, Lapi was runner-up to Natalia Zvereva in the 1987 Orange Bowl and was also a girls' doubles finalist at the 1988 US Open.

She won her first match, over Poland's Magdalena Feistel, to help Italy win the tie.

In the second round, the Italians were beaten by home side Australia and Lapi lost her match in three sets to Nicole Provis.

In 1990, she received her best ranking of 66 in the world, after making the third round at Hilton Head, in a run which included beating Claudia Kohde-Kilsch.

At the Wimbledon Championships that followed, her first-round opponent was Hana Mandliková, who had announced she would retire at the end of the tournament.