Natural systems integrate the work of many sub-units (cells) toward a large-scale unified goal (morphological and behavioral), which can counteract the effects of unexpected experiences, damage, or simply changes in tasks demands. In this paper, we exploit the opportunities presented by soft, modular, and tensegrity robots to introduce soft lattice modules that parallel the sub-units seen in biological systems. The soft lattice modules are comprised of 3D printed plastic "skeletons", linear contracting shape memory alloy spring actuators, and permanent magnets that enable adhesion between modules. The soft lattice modules are capable of independent locomotion, and can also join with other modules to achieve collective, self-assembled, larger scale tasks such as collective locomotion and moving an object across the surface of the lattice assembly. This work represents a preliminary step toward soft modular systems capable of independent and collective behaviors, and provide a platform for future studies on distributed control.