I would think that J* reporting the incident within 24 hours simply indicates that they were doing the right thing by reporting the incident ASAP. I don't think it implies anything about when the the lights were or were not on. If they were not on at the commencement of the take-off roll then that is a very serious issue. If they went out as the aircraft "took-off" then it was probably the safer option to continue.
Who is going to do a full on rejected take-off at 100kts at a place like Launy when it has suddenly gone dark? The answer is simple. Have the lights switched on manually by the ground staff for all RPT movements outside of ATC hours.