Vanguard still fits a fleet that receives the Lion class

Would HMS Vanguard still be built if the Lion-class battleships entered service?

Yes; Vanguard was part of a plan to expand toward 20-25 or ideally 27 capital ships while replacing the least modernizable R-class battleships.

The King George V class grows the fleet, Lions add modern 16-inch ships, and Vanguards replace R-class hulls that cannot be modernized economically. The target supports battle squadrons in the Atlantic, Mediterranean, and Indian Ocean, ideally with eight ships and a flagship in each theater.