I've used LT Therapy wash and it's important to know that a little of that stuff really goes a long way as it's very easy to use too much. It has moisturizers in it and if I do use it, I won't even consider applying an additional conditioner for several days. I did use the LT Therapy wash on my white Courier
*after* I
very lightly wiped the bag with a magic eraser. I have not used the LT Laundry wash - I've seen it but haven't tried it.
One thing I've learned is that there isn't one end-all-be-all conditioner, cleaner or even process that will work for every bag. I have an arsenal of stuff.. Hard core cleaners for really bad stains like mold I use RenoMat or M. Mowbrays. I know many people love saddle soap and I jumped on that bandwagon at first only to find that it can leave a weird film and I do not use it anymore.
I really like Bick 1 Leather cleaner - I put that in a small spray bottle with water (4 to 1 ratio) and spray directly on leather and wipe with a microfiber for tougher stains or cleaning. If a bag needs dunking (another controversy that has become looked down upon as well as shaming of ones that have or do), I use Woolite or Palmolive. I am a huge fan of Furniture Clinic Leather Cleaner. Doesn't leave any film whatsoever - the same as Bick 1 Leather Cleaner.
I would advise against a heavy conditioner like Blackrock or Renapur on a white bag. Stick to Bick 4 or Leather CPR.
Probably a much longer answer than what you asked. Sometimes I like to explain how the watch works as opposed to just giving the time.