@Chris Again, you are missing the point: the derivation of the LT assumes/requires isotropic light speed (it is not just a convention as frequently claimed). Any round trip assumption is only made for clock synchronization purposes. If you assume the clocks to be synchronized you don't have to bother with round trips.

@Chris Now assume, hypothetically, the speed of light to be anisotropic (e.g. in case of a moving ether). If light would move in one direction with c1=1.5c and in the other with c2=0.5 c, two observers at unit distance would time this at t1= 2/3/c and t2=2/c respectively. They would therefore derive c1=1/t1=c(1+0.5) and c2=1/t2=c(1-0.5).

@Chris As I said, it is not about round trip speed here (which does not come into it) but in determining c in contrast to c1 and c2

@Thomas Do you seriously not see the problem with assuming c1=1.5c and then using it to "prove" c1=1.5c? You can't just pick any old random velocities you want, because the round-trip speed of light is invariant in SR, regardless of any conventions.

What you are doing is akin to saying "imagine that the speed of light is 1m/s in one direction and 2m/s in the other. This doesn't work, so light must be isotropic." Just because it doesn't work for some arbitrary speeds you picked doesn't mean it doesn't work in general.

@Chris I was just giving c1=1.5c as an insider info. Of course, the observers would not know this. They just measure t1= 2/3/c and t2=2/c . But they can calculate c1=1/t1=c*3/2 and c2=1/t2=c*1/2 (assuming unit distance) so c1=c(1+0.5) and c2=c(1-0.5), or in general c1=c(1+q) , c2=c(1-q). Again, this involves one-way speeds (with clocks assumed synchronized), but unless q=0 you could not derive LT from this (this is why q=0 in Einstein's derivations).