Trump could make an argument on standing for the lawsuit because he is directly hurt by having to campaign against an ineligible candidate which costs him money.
Trump could certainly find attorneys who would construct a Constitutional argument and/or argue that naturalization laws are not controlling in this situation.
Rather than let others do his dirty work, Trump could do it himself. Trump's comments about eligibility ("attorneys have told me...") and the loan disclosure ("I have heard this is a serious issue...") come across as cowardly. If Trump thinks that these are issues, then directly accuse rather hide behind the skirts of others and snipe from the sidelines. This is his opportunity to take bold action to prove that he isn't the typical politician.
It is not Trump’s job to clear this up for Cruz. It is Ted’s job to clear it up.
He can produce his CRBA (Citizen Record of Birth Abroad) to settle it. It would prove his mother was still a US citizen at Ted’s birth.
My youngest son was born in Okinawa when my husband was stationed there in the Air Force.
Even though his birth was at an Army hospital we were required to record his birth with the US Embassy. His CRBA served as his birth certificate and was the only thing issued to us as a birth certificate.