In this paper, we define the space Sαθ (∆mv, f) of all (∆mv, f)-lacunary statistical convergent sequences of order α with the help of unbounded modulus function f, lacunary sequence (θ), generalized difference operator ∆ mv and real number α ∈ (0, 1]. We also introduce the space ωαθ (∆mv, f) of all strong (∆mv, f)-lacunary summable sequences of order α. Properties related to these spaces are studied. Inclusion relations between spaces Sαθ (∆mv, f) and ωα θ (∆mv, f) are established under certain conditions.