They believe that they are blessed if they lie to infidels.
What, they get 35 virgins for a lie, but 72 for blowing themselves up???
The long term “longevity” incentive seems rather obvious to me...
So I would summize it is preferable (to the average islamic terrorist) to lie, than to get one shot at martyrdom by turning yourself into a grease spot...
That’s just my opinion...