We have demonstrated the effect of a solvent at the second coordination sphere on slow relaxation of magnetization for hepta-coordinated cobalt(II) complexes with the formulas [Co(H4L)(DMF)(H2O)](NO3)2·(DMF) (1), [Co(H4L)(MeOH)(H2O)](NO3)2·(MeOH) (2), and [Co(H4L)(DEF)(H2O)](NO3)2 (3) (H4L = 2,2'-(pyridine-2,6-diylbis(ethan-1-yl-1-ylidene))bis(N-phenylhydrazinecarboxamide). Structural analysis reveals that the presence of lattice solvent molecule in 1 and 2 dramatically changes the crystal packing and noncovalent interactions as compared to 3 where no solvent molecule is present in the crystal lattice. The dc and ac magnetic susceptibility measurements reveal the presence of easy-plane magnetic anisotropy for all the complexes, and field induced slow relaxation behavior has been observed above 2 K for 1 and 2 in contrast to 3 due to the availability of the solvent molecules in the crystal lattice. The ab initio calculations further support the sign of D and the negligible effect of the first co-ordination sphere, as almost similar D values were obtained for all the complexes. The field and temperature dependence of relaxation time confirm that quantum tunnelling of magnetization (QTM) plays a major role in slow magnetic relaxation, and thermal dependence like an optical or acoustic Raman pathway is also important. To further analyze the effect of dipole-dipole interaction on slow magnetic relaxation, a dilution experiment has been performed.