Localized supersonic long-living nonlinear modes excited in triangular lattices of point particles interacting via potential Morse bonds are studied in a frame of a model with appropriately chosen bonds to rule out redundancy bonds. Numerical simulations on a base of Newtonian equations are performed to define configurations (coordinates and velocities of all particles) of steady-state (meta-stable) modes and their characteristics including in particular excitations being lump soliton-like.