  We investigate scattering of lattice laser radiation in a strontium optical
lattice clock and its implications for operating clocks at interrogation times
up to several tens of seconds. Rayleigh scattering does not cause significant
decoherence of the atomic superposition state near a magic wavelength. Among
the Raman scattering processes, lattice-induced decay of the excited state
$(5s5p)\,{}^{3}\mathrm{P}_{0}$ to the ground state
$(5s^2)\,{}^{1}\mathrm{S}_{0}$ via the state $(5s5p)\,{}^{3}\mathrm{P}_{1}$ is
particularly relevant, as it reduces the effective lifetime of the excited
state and gives rise to quantum projection noise in spectroscopy. We observe
this process in our experiment and find a decay rate of $556(15)\times
10^{-6}\,\mathrm{s}^{-1}$ per photon recoil energy $E_\mathrm{r}$ of effective
lattice depth, which agrees well with the rate we predict from atomic data. We
also derive a natural lifetime $\tau = 330(140)\,\mathrm{s}$ of the excited
state ${}^{3}\mathrm{P}_{0}$ from our observations. Lattice-induced decay thus
exceeds spontaneous decay at typical lattice depths used by present clocks. It
eventually limits interrogation times in clocks restricted to high-intensity
lattices, but can be largely avoided, e.g., by operating them with shallow
lattice potentials.
