The phrase "lead to illness" is correct and usable in written English.
You can use it to describe how an activity or behavior can result in someone becoming ill from a sickness or disease. For example, "Exposure to germs and bacteria can lead to illness."
And even infected eggs don't necessarily lead to illness.
Too often, the burdens of caregiving lead to illness, stress and depression.
That assessment concluded that even low levels of exposure to particulate matter can lead to illness and death.
These valuable micronutrients have an antioxidant effect, which helps neutralise changes in cells that might lead to illness and disease.
Novel disinfection methods are being sought to provide additional means of protection in a number of areas where disease outbreaks could lead to illness or fatalities.
Exacerbation of a particular dosha, through eating the wrong foods or living the wrong physical or emotional lifestyle, will lead to illness.
Many scientists believe that abnormalities in brain chemistry cause depression, but they have not established what these abnormalities are or how they lead to illness.
Following this, when developers consider new tools or technologies, they must ask several vital questions, such as "Does it foster health or does it lead to illness?
Antioxidants are thought to protect cells from damage and mop up free radical molecules, which may lead to illnesses such as cancer and heart disease.
For most people, influenza infection is just a nasty experience, but for some it can lead to illnesses that are more serious".
This way the stress response becomes maladaptive, causing a plethora of negative physiological effects on the body which lead to illnesses.
