He posted the file to me. It was impossible to attach here as it is 9Mb+.
To me, the intersection seems to be pretty smooth (regarding SketchUp1s nature to segmenting everything) but if really smooth results are needed, you need to make everything so detailed. The arch was made of really high segmented arcs, the dome way made of a really high segmented arc as the face to be lathed however the circle around which you lathed it is still the default 24 segmented circle.
Such an intersection will always be somewhat segmented but if you are ready to sacrifice workability for smoothness and precision, you need to do it including all elements of the model.
ConcreteDome1_TelkerDesign.png