dude A sees it at the same time. Dude B sees the lightning at the front first then the one at the back from his eye on the back of his head. because the train gets shorter (I think).
Your conclusion that Observer A on the platform observes both events ocurring simultaneously (at the same time), while Observer B in the train observes lightening strike the Front BEFORE the Back of the train is correct, however your reason is not.
Observer A sees both events happening at the same time because the speed of light is constant, and has the same amount of distance to travel to reach observer A, hence the time that the light from each event reaches the eyes of Observer A is the same [note we 'observe' events happen when the light from that event reaches us, e.g. a bomb explosion or lightening srike]
However, for Observer B, who is on a "train travelling at a high speed" [we assume to the right on the page, in which the arrow is pointing towards], the light from the back needs to travel to the right to reach Observer B, while the light from the front og the train needs to travel to the left. However, the light takes some time to travel this distance, no amtter how small. in this time, Observer B would have moved to the right ever so slightly, since he/she is on a train tarvelling to the right. this means it moves closer to the point where the lightening struck at the front of the train,a nd further from the one at the back. So, to reach Observer B, light from the front has to travel a shorter distance than the light from the back (since Observer B moved closer to where the front lightning was and away from where the back lightning was - can't stress this enough). but light travels ata constant speed, so it takes longer for the light from the back strike to reach Observer B than the front. So Observer B sees the Front of the train as being struck by lightning BEFORE the back.
This is the relativity of simultaneity, and has nothing to do with length contraction.
Hope that helps.
