Rhetorical question. A lattice is an infinite array of geometrical points in the space where each point has identical surroundings to all others. Hence a lattice is an abstract mathematical concept. The crystal structure is a real object, obtained by convoluting the lattice with a basis (an atom or a group of atoms).
So why to use misleading definitions such as lattice vibrations, lattice energy, or simply ‘lattice’ instead of ‘structure’?
In most cases it can be understood if ‘lattice’ actually refers to ‘structure’, but in some particular cases this ambiguity is really confusing. A practical example from literature. The concept of nematicity in crystalline materials was introduced in [Nature 393 (1998) 550]; considering a 2-dimensional square lattice “The nematic phase breaks the four-fold rotation symmetry of the lattice, but leaves both translation and reflection symmetries unbroken”. This is clearly impossible for a lattice (reflection symmetries are generator for the four-fold rotation), but not for a real crystal structure (for example an orthorhombic structure with pseudo-tetragonal metric). So the doubt is: did the author gave this definition having in mind a lattice (and in this case their theory must be rejected) or a crystal structure?
About the confusion between lattice and crystal structure see: https://journals.iucr.org/j/issues/2019/02/00/to5189/index.html