LAMMPS currently does not have a way to calculate elastic constants and bulk moduli directly. The new triclinic geometry enables future fixes to do just that. In the upcoming package we will be adding a general NpT ensemble. Variations in shape stemming from application of this fix will allow you to deduce the compliance and from it the elastic moduli. You can add a general NpT ensemble through a fix. Shape measurements could be done either through a fix or the new compute functionality.