The appointment follows the departure of former Lloyd's comms head Peter Fitch, who left the insurance market to join Blue Rubicon as a board director earlier this year.
Lassalle joined yesterday from Actis, a global private equity firm with $6bn funds under management in Africa, China, Asia and Latin America, where she was head of comms.
Before that she was chief marketing officer at global executive search firm Heidrick & Struggles, based in the US.
Lloyd's chief executive Inga Beale said: "Tashi's marketing and communications expertise in domestic and high growth markets will enable us to reach new global audiences as we deliver on our long-term growth strategy.
"Tashi brings a fantastic blend of skills to the role, which I'm sure will continue to build on the work the communications team delivers for Lloyd's around the world."
Lassalle said: "Lloyd's is an iconic organisation with a distinguished history. I'm pleased to play a role participating in the market's modernisation, global growth and continued industry leadership, and hope my prior experience will contribute to Lloyd's sustained success."