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The generalisation of Fibonacci sequence introduced by Edson in 2009. After the generalisation of Fibonacci sequence, Bilgici introduced generalized Lucas sequences. In 2016, Yilmaz and Coskun introduced generalisation of Fibonacci and Lucas polynomials which is known as bi-periodic Fibonacci polynomial and bi-periodic Lucas polynomials. In 2020, Verma and Bala defined bi-variate bi-periodic Fibonacci polynomials. Now, We have defined Bi-variate Bi- periodic Lucas polynomials for with initial conditions by the recurrence relation and We have obtained generating function for defined polynomial and found nth term of the . Investigated relationship between Bi-variate Bi-periodic Fibonacci and Bi-variate Bi- periodic Lucas polynomials. We derived some most popular identities like Cassini’s identity, Catalan’s identity, d’Ocagne’s identity and binomial sum. Convergence of two successive terms of Bi-variate Bi-periodic Lucas polynomial is also discussed.