Does a lab specialization count for computing the bonus due a magical focus? I'd say no, that any lab bonus is only counted once.
Assume a maga is creating a longevity ritual, with an applicable focus. The area has a magical aura of 3, the maga has an Int of 3, magic theory of 6, Creo of 15 and Corpus of 10. Her lab has a creo specialization of 1, and corpus specialization of 2.
I'd expect her total to be 3+6+3+(15+1)+(10+2)+10 = 50, not 52.
No. The lab specialization adds to the lab total, not to the Art. The Art is added again to the lab total from the Magical Focus. Puissant Art is different because that actually adds to the Art, so when adding the Art again it gets included as well.
The particular one you've got is
Int 3 + MT 6 + Aura 3 + Creo 15 + Corpus 10 + Focus 10 + Lab (1+2) = 50