If you use Reach to Interrupt the Battle (to interrupt Nero's ongoing immunity), then yes. Cards that say "May do X, do Y, and do Z" or similar (like "You may interrupt the battle, draw three cards, and play the next enhancement") means "You may do X. Then you may do Y. Then you may do Z." So you have a choice at each step.
However, if you choose to ITB, then you interrupt ALL ongoing abilities, including Lydia's play-other-enhancements ability. She cannot then play Purple off of Reach's play ability. Reach stays played, but you'd have to use White in that case.
