Laziness and sleepiness are so similar that there must be another reason than being lazy or tired. It's constipation.
People need to get a good diet that includes probiotics, so that they stay regular. One help is black seed oil... nigela sativa... black cumin oil. It fights the parasites in the body so that probiotics can work easier.

Though, sleepiness is a condition due to the lack of proper rest. While laziness is a behavior which is contrary to the expectation or people being eager to work and make a living off their abilities and skills.
Even though I could agree having a healthy gut is always good for one's being wellbeing, I am not sure whether it has something directly to do with the pack of sleep or the behavior of a person when comes to working.
If you have the source of this theory of yours about the relation between probiotics and sleepiness and laziness, I would be happy to give a look to it.