How do I politely tell an owner that they have to train their dog?

Basically, I'd have the conversation (and have had some similar ones) by focusing it on observation and safety.

Something like what you've already written: You really care about the dogs' well being and enjoy spending time with them. For safety reasons, you can't walk both of them at the same time as the lab is very strong and can overpower you on a walk, leading to an unsafe walk for both of you. You've done some training, and clearly the dog shows it is adaptable to change, but in order to be effective, it has to be reinforced on every walk. (I would not necessarily say that training & respect is needed b/c what you really mean is a change to safe walking).

When you wait & allow the owner to respond, they may be in complete agreement and ask if you can suggest anyone who can work with them to get results or if that's something you do. If they don't see the need, it could lead to them searching for another walker, but if you speak from a what's best for Rover standpoint, it doesn't seem likely that you'll get a bad review. If the dogs end up going to another sitter as a result, just know you did the right thing rather than continue, knowing the odds were stacking up against you , that one time it could lead to something tragic beyond your control.

Honestly its rare the owners will train if the dog is grown and misbehaving. Think. If the dog is 5,6,7 years old and they've had since a puppy....that means that dog has been doing that for years. Most dogs respond quickly to training, its the owners job to stick to it. So if the dog didn't have manners with you, imagine how they are with owners?! Yesh. Try it, but you might have to just skip them next time. Unless, of course, you're okay with retraining the dog. I've had some dogs where they got so used to my rules that even though they reverted back to bad manners with owners, when they came back to me they still remembered to be respectful. And after day or two were obedient again. Just depends on if you're okay with the possible bad behavior returning and retraining sessions.