Glad you asked; I am probably one of the prime apostles re the brake light switch dogma. The link below is to my treatise on it. If there is any good news, you do not have a Toyota where a brake light switch concern leads to no start.
Somehow LR avoided that - you just get nasty messages such as "replace the tranny", "there is no hope", "all is lost", "cruise control not available" and other messages of that sort but at least your 3 does start and will still go places - well the Toyota's do to, but it is to the dealer on the top of a flat bed.
The fact you are having starting problems is why I did not mention the switch but while you are fooling around, and once you get the starting problem sorted out, then yes, I would replace the brake light switch just because it will cause problems in the future. For me, I noticed that cold weather, as in below freezing is when the nasty messages start to appear when the switch is tired and unhappy.
DISCO3.CO.UK Photo Gallery - Brake Light Switch Replacement