Can someone with a down syndrome get rid of his lazy eyes?

Maybe, if a child: A lazy eye is the weaker eye that the brain is not using much, because the image from the weaker eye is a lot different from the image from the good eye. A pediatric ophthalmologist (eye specialist) can check the eyes and see if one is actually "lazy", sometimes, glasses, patching, or other treatment can be done. Strabismus (eyes looking in separate directions) is different from "lazy eye".

Possibly: Down syndrome does not prevent you from being treated. The issue is related to the cause of the lazy eye. If the eye is not straight, it can be surgically corrected if the child is young enough. If the lazy eye is prescription-related, it can be treated with glasses and/or patching as long as the patient can tolerate it.