Lexington battlecruisers as large scouting cruisers

Could the Lexington-class battlecruisers compete with Renown or Hood?

Not in a direct comparison, because Lexington was optimized as a fast scouting and commerce-warfare cruiser rather than an armored battle-line fighter.

Lexington's intended work was fast scouting and economic warfare. That role makes the earlier British Invincible concept a closer comparison than a direct contest with Hood or Renown. The design combined extensive subdivision, reliable turbo-electric machinery, and powerful 16-inch guns. Its armor and protective coverage were the weaknesses in a battlecruiser engagement. A British design intended to defeat such large scouts, exemplified by G3 in the comparison, would be fighting the kind of opponent it was designed to overcome.