You need to set an initial condition to upset the symmetry. Set the initial voltage on one of the bases to zero volts. I don't know how you do that with Livewire, but I'll bet it is possible. In SwitcherCAD III, you set a .IC condition.
AG's suggestion of using a PWL battery should also work. As he said, turn it on with a fast risetime.
You should also add a 2k resistor from each collector to +V, so the collector voltage will get all the way up to +V. As Audioguru said, you may not get much current through the LEDs, depending on what color they are.