Assume M and M' are the origins of 2 frames and in the M' frame, there is an observer C' located at $$(\frac{-vd'}{c},0,0)$$ with $$d'>0$$.

When M and M' are co-located, lightning strikes their command location.

Here is the question, when C' and M are co-located, where is the lightning along the positive x-axis for both frame coordinate systems?

First, we have to know the time on the clocks at M and C' when they are co-located.

M frame calculations.

1) M clock - Apply LT $$x'=(x-vt)\gamma$$ with $$x'=\frac{-vd'}{c}$$ and $$x=0$$. Then, solve for t so $$t=\frac{d'}{c\gamma}$$

2) C' clock. Apply LT $$t'=(t-vx/c^2)\gamma$$ with $$t=\frac{d'}{c\gamma}$$ and $$x=0$$. Then $$t'=\frac{d'}{c}$$

M' frame calculations

1) C' clock - Apply LT $$x=(x'+vt')\gamma$$ with $$x'=\frac{-vd'}{c}$$ and $$x=0$$ and solve for t'. Then, $$t'=\frac{d'}{c}$$.

2) M clock - apply LT $$t=(t'+vx'/c^2)\gamma$$ with $$t'=\frac{d'}{c}$$ and $$x'=\frac{-vd'}{c}$$. Then, $$t=\frac{d'}{c\gamma}$$.

So far so good. SR agrees in the calculations of both frames the times on the clocks at C' and M when the two are co-located.

Now we ask the question where is the lightning along the positive x-axis when C' and M are co-located?

M frame calculations for the space-time coordinates of the lightning along the positive x-axis when C' and M are co-located.

1) M coordinate system location. Since the time on the M clock is $$t=\frac{d'}{c\gamma}$$, apply the light postulate $$x=ct$$. So, $$x=d'/\gamma$$.

Thus, the space-time coordinate of the lightning in the M coordinate system is $$(d'/\gamma,0,0,\frac{d'}{c\gamma})$$

2) M' coordinate system location. Apply LT $$x'=(x-vt)\gamma$$ and $$t'=(t-vx/c^2)\gamma$$ with $$x=d'/\gamma$$ and $$t=\frac{d'}{c\gamma}$$. Then, $$x'=d'(1-v/c)$$ and $$x'=d'(1-v/c)/c$$.

Thus, the space-time coordinate of the lightning in the M' coordinate system is $$(d'(1-v/c),0,0,d'(1-v/c)/c)$$

M' frame calculations for the space-time coordinates of the lightning along the positive x-axis when C' and M are co-located.

1) M' coordinate system location. The time on the clock at C' is $$t'=\frac{d'}{c}$$. The lightning struck at M', so apply the light postulate from M', which is also the origin of the primed frame $$x'=ct'$$, with $$t'=\frac{d'}{c}$$. Then, $$x'=d'$$.

Thus, the space-time coordinate of the lightning in the M' coordinate system is $$(d',0,0,d'/c)$$

2) M coordinate system location. Apply LT $$x=(x'+vt')\gamma$$ and $$t=(t'+vx'/c^2)\gamma$$ with $$x'=d'$$ and $$t'=\frac{d'}{c}$$. Then, $$x=d'\gamma(1+v/c)$$ and $$t=d'\gamma(1+v/c)/c$$.

Thus, the space-time coordinate of the lightning in the M coordinate system is $$(d'\gamma(1+v/c),0,0,d'\gamma(1+v/c)/c)$$.

Conclusions:

When C' and M are co-located, SR claims the lightning is located at M frame space-time coordinates of $$(d'/\gamma,0,0,\frac{d'}{c\gamma})$$ and $$(d'\gamma(1+v/c),0,0,d'\gamma(1+v/c)/c)$$.

When C' and M are co-located, SR claims the lightning is located at M' frame space-time coordinates of $$(d'(1-v/c),0,0,d'(1-v/c)/c)$$ and $$(d',0,0,d'/c)$$.

Therefore, if these calculations are correct, then SR claims when M and C' are co-located, one lightning strike is located at 2 different positions along the positive x-axis in both coordinate systems, which of course is inconsistent with nature.

So, where is the error in the calculations?