Final answer:
The lineage that does not contain photosynthetic bacteria is Spirochaeles.
Step-by-step explanation:
Of the given options, the lineage that does not contain bacteria that are photosynthetic is Spirochaeles. Spirochaeles belong to the phylum Spirochaetes, which includes spiral-shaped bacteria. These bacteria are not capable of photosynthesis.
On the other hand, Cyanobacteria are photosynthetic bacteria and are capable of oxygenic photosynthesis. Actinobacteria and Proteobacteria include some photosynthetic bacteria as well.