Despite Israel designating Jerusalem as its capital, Britain has long maintained its embassy in Tel Aviv.
A Downing Street spokeswoman said Ms Truss told Mr Lapid “about her review of the current location of the British embassy in Israel”.
She made the pledge during the Tory leadership contest in a letter to the Conservative Friends of Israel.
Ms Truss said she understood the “importance and sensitivity” surrounding its location.
The leaders discussed a range of issues at their first meeting since Ms Truss succeeded Boris Johnson as Tory party leader and prime minister earlier this month.
Among the topics touched on were efforts to strengthen bilateral ties between Israel and Britain. They agreed to establish teams to negotiate a free-trade deal as quickly as possible.
Mr Lapid also broached the subject of Iran, urging Ms Truss to abandon the nuclear deal and instead begin talks with Tehran for a better agreement that would prevent the nation from becoming a nuclear state.
Following their discussion, Mr Lapid posted a message on his personal Twitter account to thank his "good friend" Ms Truss, saying she "announced that she is positively considering moving the British Embassy to Jerusalem, the capital of Israel".
"We will continue to strengthen the partnership between the countries," he said.
The office of Israel's prime minister tweeted that he had "expressed confidence" to Ms Truss that under her leadership ties between the two countries "will reach new heights in various fields, in particular the economy, innovation and security".
"PM Lapid emphasised to PM Truss the necessity of avoiding further compromises with Iran, and further emphasised that Israel’s expectation is the advancement of a longer and stronger deal that will provide a response to the full range of threats stemming from Iran," it added.
In December 2017, Mr Trump's announcement that he would move the US embassy from Tel Aviv to Jerusalem was widely condemned by critics who said it would inflame tensions in the region.
Both Israelis and Palestinians claim the city as their capital.
The new US embassy was opened in Jerusalem in May 2018, leading to violent clashes between Palestinian protesters and Israeli security forces on the Gaza border. Dozens of Palestinians were reported to have been killed and thousands wounded by Israeli troops at the border fence.