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We propose to realize controllable squeezing states of ferromagnetic magnons with a spinor Bose-Einstein condensate confined in an optical lattice.We use an external laser field to induce optical dipole-dipole interaction, which leads to magnon excitations of the system.By focusing on the role of the long-range magnetic and the optical dipole-dipole interactions, we show that the existence and properties of the produced squeezed magnons can be well controlled by tuning the transverse trapping widths of the condensates.We also show that the magnon excitations in this system have a close analogy with the dynamical Casimir effect at finite temperature predicted by Plunien et al.[Phys.Rev.Lett.84, 1882 (2000)] and Jing et al.[Phys.Lett.A 268, 174 (2000)].