The interaction of laser beams carrying phase singularities, namely vortex beams, with turbulent media has been of interest due to its relevance in many areas such as free space optical communications, quantum communications, optical tweezers and so on. In the past several years, the evolution properties of different laser beams have been studied related to the propagation factor and effective radius of curvature. The propagation factor is an important factor forvaluing the propagation beam quality in practical application, and the radius of curvature of laser beams is an important parameter for describing beam wavefront properties. On the other hand, the turbulent ocean is also a distinct turbulent medium, while the propagation of the ocean depends on the salinity fluctuation and temperature of the ocean turbulence. In present paper, the partially coherent Lommel-Gaussian Beam (PCLGB) is chosen as an example, which is a typical non-diffracting beam, and the transverse intensity shape can be conveniently regulated by a symmetry parameter. By the use of Wigner distribution function, analytical formulas of the propagation parametric of the PCLGB and partially coherent Bessel-Gaussian beam (PCBGB) through turbulent ocean are derived. Propagation properties of the effective radius of curvature and the propagation factor of PCLGBs through turbulent ocean are explored numerically.It is shown that the propagation properties of the PCLGBs are as same as that of the PCBGBs, but the continuously variable orbital angular momentum make it more superior to the latter. The properties of the PCLGBs depend on the oceanic parameters. As relative strength of temperature and salinity fluctuation, and the rate of dissipation of mean-square temperature are smaller, or the rate of dissipation of turbulent kinetic energy per unit mass of fluid is larger, the effective radius of curvature is larger and the propagation factor is smaller, namely, the effect of turbulence on the beam is smaller. The work can provide theoretical and experimental basis for practical applications of underwater laser communication and laser weapons.