The recent experimental realization of a three-dimensional (3D) optical lattice clock not only reduces the influence of collisional interactions on the clocks accuracy but also provides a promising platform for studying dipolar many-body quantum physics. Here, by solving the governing master equation, we investigate the role of both elastic and dissipative long-range interactions in the clocks dynamics and study its dependence on lattice spacing, dimensionality, and dipolar orientation. For small lattice spacing, i.e., $k_0all 1$, where $a$ is the lattice constant and $k_0$ is the transition wavenumber, a sizable spin squeezing appears in the transient state which is favored in a head-to-tail dipolar configuration in 1D systems and a side-by-side configuration in 2D systems, respectively. For large lattice spacing, i.e., $k_0agg 1$, the single atomic decay rate can be effectively suppressed due to the destructive dissipative emission of neighboring atoms in both 1D and 2D. Our results will not only aid in the design of the future generation of ultraprecise atomic clocks but also illuminates the rich many-body physics exhibited by radiating dipolar system.
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