This varies from state to state, but in many states, a stairlift falls under "home modification" covered by Medicaid Home. However, you may need to fall within a certain income bracket to be eligible for it. You may wish to get confirmation from your state's Department of Health and Human Services if you are unsure.
While private health insurance do not often cover home modifications, you may be eligible for some claims if your disability is caused by a work-related accident, for instance. Seniors may be covered under long-term care policies, although it is best to check with your insurance provider.