No, it is not one of the four ‘official’ responses which are
- Christ has died, Christ is risen, Christ will come again.
- When we eat this bread and drink this cup we proclaim your death Lord Jesus, until you come in glory.
- Dying you destroyed our death, rising you restored our life, Lord Jesus, come in glory.
- Lord, by your cross and resurrection you have set us free. You are the savior of the world.
The piece you speak of is actually the refrain to a song that was popular in the 1960s (I know this because I was in the childrens’ choir at my church in Philadelphia and remember singing this between 1967 and 1970). There were several little verses that went with it, like “in him, all our sorrow, in him all our joy”, “If we die with the lord, we shall live with the Lord”, etc. etc. ad infinitum.
Apparently quite a few parishes coapted this ditty in the 80s and 90s, and it still strikes terror (I mean, still is used) today despite the GIRM and pastoral letters from bishops flying out which require only one of the four responses above.
You could google the GIRM or Redemptoris Sacerdotalis (sp?) which may be long but which will give you the ‘paper’ information about the four legitimate responses, and offer it to your priest/choir director. But be prepared to hear either, “The bishop says it’s ok”, “that is just a suggestion, not an order”, or "Fr. says it is ok because it falls under ‘tradition’, or some variant thereof.
