The time dependant transformation equations we present are not actually Lorentz group. We are calling them that because they look and work so much like the Lorentz transformation equations. But, to be precise they are a case of the Poincare group.
Special relativity can deal with accelerated frames to an extent.
MTW Pg173 show how a local coordinate transformation relates an accelerated frame's coordinates to a local inertial frame's coordinates. Unfortunately for time dependant a the coordinate transformation above is only good locally. However, I found a global coordinate transformation for which this invariant interval is the good result globally. It looks a lot like the Lorentz transformation equations. These are Lorentz transformation equations modified to handle an accelerated frame.