Could British fuel management have saved Lexington?

Would Lexington have survived with a British-style aviation-fuel management system?

Yes, assuming an equivalent system had been installed. Fitting it would have required substantial redesign, extra cost, and more construction time.

The comparison is with systems fitted to Courageous and Glorious in the late 1920s and early 1930s. An equivalent installation would have altered a large part of Lexington's ship systems. The US Navy had limited time and money while building her and would also have needed a reason to accept those costs before experiencing this loss. The proposed survival therefore depends on substantial changes to the design.