Britain uses American yards for repairs, not a replacement building program

If Japan gains the Pacific, does the Royal Navy begin ordering capital ships and cruisers from American yards?

No; Britain would more likely complete the Lions and send additional ships to American yards for repair.

Wholesale British orders for capital ships and cruisers from American yards seem unlikely. Completion of the Lion-class battleships is the expected course. American industrial capacity would be especially useful for repairing British ships when domestic yards were overloaded or distant from the theater. Emergency repair cooperation would leave British design and construction of the core fleet in place.