What I find difficult to understand is that this is a critical take-off, and yet the crew seem to be quite jovial about it all. The higher stress level and seriousness of the situation seems to escape them. The confusion over the first or second turn right is passed off with light hearted banter and amusement.
I don't see the light issue playing a major part here. The runway was NOTAMed off and a warning given on the ATIS. From the CVR the crew is well aware which runway they require and the fact that it is the second right.
There are many things in the transcript to be disturbed about.