A lot of good info on this site, I’m sure some people will come to tell you to use the search bar.
On a basic level, if by live resin sauce you mean the high terpene fraction, a pretty standard formulation is to add about 30% of the sauce to distillate and mix. You want to heat the sauce as little as possible to retain terps, so no decarb. Some thca in a cart is fine, even good for the consistency of the oil. The distillate should keep the oil in the cart from crystalizing.
If you have a nice live resin sauce, I see no need to add additional cannabis derived terps.
Hope you fan find some of the other good threads on this topic.