The sudden senior departures from Kinnect has prompted calls for Lloyd's to overhaul the platform.
Last week chief executive Toby Davies and executive chairman Iain Saville resigned, raising questions over Kinnect's future.
A senior market figure said: "Perhaps Lloyd's should go back to the drawing board to start simplifying the system.
"Nick Prettejohn [Lloyd's chief executive] has put a lot of his own credibility on the line for this - if he doesn't make it, this could be the end of the Prettejohn regime."
Another Lloyd's source said he hoped the project would become "less ambitious and simpler".
A Lloyd's spokeswoman said that despite the departures "Kinnect continues to move forward at a good pace".
Michael Dawson is to take over as interim chairman and Nick Prettejohn as non-executive board member. Steven Haasz, head of change management, will provide "additional executive support".
Saville will stay on in a part-time advisory role.