This is because the presence of atoms in the cavity shifts the cavity resonance and hence the depth of the intracavity lattice: the Bloch energies are dependent on the potential depth.
(a) any measurement of the output field will generate backaction onto the condensate (Mekhov, J. Phys. B: Atomic, Molecular and Optical Physics, 45(10), 102001). This will generate extra noise, but might also help as it reduces atom number uncertainty in the cavity.