I think you are missing the point slightly, yes. The Galilean and Lorentz transforms link measurements made in different frames, and the example you give of "Galilean velocity addition" is not a frame change.
There are two distinct concepts related to relative speed. One is the rate of change of distance (aka the "separation rate") between two objects measured using some frame (not necessarily the rest frame of either). In this case you can just add speeds relative to this frame. But this is a separate concept from relative velocity, the velocity A measures B to have. To get that, you need to use the velocity transform to calculate B's velocity in A's frame.
That distinction can be made in either Newtonian or Einsteinian physics, but is a distinction without a difference in the Newtonian case because the Galilean velocity transform is so simple.
So in your example, if the pedestrian wants to know the time he has until the cars collide then he uses the separation rate. However, if he wants to know the time the drivers will measure until collision he needs to Lorentz transform the positions and velocities into the rest frame of one car and then apply the separation rate in that frame (which should be easy as one car's velocity will be zero). You aren't using the Galilean transforms at all.
"Domain of applicability" is a slightly different concept. It usually refers to the range of velocities/energies/whatever over which an approximate theory (e.g. Newtonian physics) is indistinguishable from a more precise one (e.g. relativity). To work that out you usually Taylor expand something, find that the first term is the simpler theory, and look at when the second term is measurable to your degree of precision. So Lorentz velocity addition says$$\begin{eqnarray*}
u'&=&\frac{u+v}{1+uv/c^2}\\
&=&(u+v)\left(1-\frac{uv}{c^2}+\ldots\right)
\end{eqnarray*}$$You can see that ignoring all terms in the series after 1 gives you Galileo, so Galilean transforms are fine as long as speeds are low enough that a fractional error of ##uv/c^2## in your velocity measurements is tolerable.
