Abstract: As a sequel of the first part, we will continue to talk about Furstenberg Theory (e.g. Furstenberg type formula, Kifer non-random filtration, Furman-Furstenberg criterion for positivity of LE, etc.) in our mixed setting. Moreover, we will provide several interesting applications regarding the positivity and continuity of the Lyapunov exponent. This is a joint work with Pedro Duarte and Silvius Klein.