The presence of superlattice reflections and detailed analyses of the powder neutron and x-ray diffraction data reveal that La rich (BF$_{0.50}$-LF$_{0.50}$)$_{0.50}$-(PT)$_{0.50}$ (BF-LF-PT) has ferroelectric rhombohedral crystal structure with space group textit{$R3c$} at ambient conditions. The temperature dependence of lattice parameters, tilt angle, calculated polarization $(P_{s})$, volume, and integrated intensity of superlattice and magnetic reflections show an anomaly around 170 K. Impedance spectroscopy, dielectric and ac conductivity measurements were performed in temperature range $473K leq T leq 573K$ to probe the origin of large remnant polarization and frequency dependent broad transitions with large dielectric constant near $T_c^{FE}$. Results of impedance spectroscopy measurements clearly show contributions of both grain and grain boundaries throughout the frequency range ($10^{3}$ Hz$leq fleq 10^{7} $ Hz). It could be concluded that the grain boundaries are more resistive and capacitive as compared to the grains, resulting in inhomogeneities in the sample causing broad frequency dependent dielectric anomalies. Enhancement in dielectric constant and remnant polarization values are possibly due to space charge polarization caused by piling of charges at the interface of grains and grain boundaries. The imaginary parts of dielectric constant ($epsilon^{primeprime}$) Vs frequency data were fitted using Maxwell-Wagner model at $T_c^{FE}(sim 523$K) and model fits very well with the data up to $10^{5}$ Hz. Magnetodielectric measurements prove that the sample starts exhibiting magnetoelectric coupling at $sim 170$ K, which is also validated by neutron diffraction data.
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