First order of business - drop those names. They're not necessary in the logline.
You've given us the flawed protagonist - a washed up archaeologist. You've given us his ruthless rival.
The event; the discovery of a lost city of immeasurable wealth ...
What is the action that forms the bulk of the story? What are the stakes of failure - just the loss of potential wealth?
Also, this bears contemplation at this stage - obviously this is meant to have an Indiana Jones/Tomb Raider/National Treasure vibe to it (what with the title and all) ... but what sets it apart and makes it unique compared to those franchises? What's the fresh take on the old format?