Is Lysol Disinfectant Spray healthier than a natural deodorizer?

The nearest thing to a "natural deodoriser" is not to bath and to live that way till your skin microbes settle down. That works surprisingly well for many people, but it is not suitable for most urban needs. It is cheap though, as long as it does not interfere with your social success.

ANYTHING else you do is artificial by definition, even just washing with soap.

Washing should PRECEDE EVERY kind of deodorisation; the idea is to get rid of all your smelly stuff before you proceed to prevent new smells from developing. It is no good just trying to cover up the dirt, naturally or otherwise!

There are several basic types of artificial deodoriser:

Washing: Is that what you meant by "natural"? If it works for you and your skin can take it, washing with soap or other detergents is good, but you may have to do it several times a day. It isn't enough for most adults though, especially if they do sweaty work.

Scents and other stuff that drowns out the smell: These simply are ways of staying dirty and smelling of scent plus dirt. Often herbal scents. Not natural anyway.

Stopping the smell from spreading: Another kind of "natural" that isn't really natural is to treat the strategic areas with a substance (available as SOME BRANDS of "cream", or more "naturally" with an alum "crystal", which works very effectively if applied suitably and is which not (repeat NOT, and I don't have shares in the stuff!) toxic on one's healthy skin, no matter what people say). These are some of the best deodorants, as long as you start daily with well-washed skin. May not be enough for marathons or sweaty heavy work in hot climates.

Finally there is disinfection: If Lysol works for you it is OK. It is not at all dangerous if you don't drink it or get it in your eyes or let children or pets get at it. It should be applied to strategic areas after washing. IF it works for you it does so by killing bacteria in the sweat pores. One's own personal body odour is not really your own, but the product of bacteria rotting sweat, dead skin cells and so on. The trouble is that not many antiseptics and disinfectants are effective in stopping this process. One used to be able to get Hexachlorophene preparations (such as a product called Phisohex), that worked amazingly well for years, but it was discovered to be poisonous, especially to small children, and as far as I know it is now unavailable to the public in first-world countries.

And as I said, natural deodorants aren't natural, so don't enrich people who tell you that they are natural in order to get your money.