Layer-dependent electronic structures and magnetic ground states of polar-polar <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>LaVO</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>KTaO</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></m

Employing a first-principles and model Hamiltonian approach, we work out the electronic properties of polar-polar LaVO$_3$/KTaO$_3$ (LVO/KTO, 001) heterostrctures, with up to six layers of KTO and five layers of LVO. Our analyses indicate the existence of multiple Lifshitz transitions (LTs) within the $t_{2g}$ bands, which can be fine-tuned by adjusting the number of LVO layers or applying gate voltage. Contrary to the experimental report, spin-orbit coupling is found to be negligible, originating solely from the Ta $5d_{xy}$-derived band of KTO, while the 5$d_{xz}$ and 5$d_{yz}$ bands are considerably away from the Fermi level while LVO overlayers having no role in it. Magnetic properties of the heterostructures, due to Vanadium ions, exhibit a pronounced sensitivity to the number of LVO and KTO layers. Our calculations indicate that the interlayer AFM, (so called A-AFM), is energetically most favorable. This is further supported by ground state energy calculations on extended $\sqrt{2}\times\sqrt{2}$ supercells. Moreover, we find that an insulator to metal transition at the interface requires four LVO layers, corroborating the experimental observation. The interfaces featuring ferromagnetic (FM) ground states turn out to be \textit{half-metallic} after the critical thickness is reached. Considerations of the magnetic interactions appear crucial for the experimentally observed critical thickness for metallicity.