IANAL, but if the author of the program author claims any copyright over the program's output, it is presumably the case case that the program outputs part of itself. but if the entire program claims to be licensed under LGPL, then no part of it is under CC-BY-NC, and more, no part of the licensing terms demand the output portion to be relicensed under CC-BY-NC, so the origin of that statement is hard to guess. there appears to be a contradiction or missing information (e.g., it's not the whole program that's under LGPL), which makes it hard to make any safe recommendations.
it is certainly the case that if you modify the program so that its output no longer contains parts of the program itself (or of any other material copyrighted by the author), then you could remove that statement. but don't take that statement as a restriction, it is either a statement of fact, or some misconception from an author that doesn't understand copyright. the latter is more common than the former, alas.
is contacting the author for clarification a viable plan?