Yes, as far as I know the lottery is independent of anything else, but you should check the USCIS website and consult an immigration lawyer.
Be careful with the lawyer: try and get one through a recommendation of someone you trust who has used their services. Because of the high demand for immigration into the United States, there are many unscrupulous people involved in such matters.
Be careful with the lawyer: try and get one through a recommendation of someone you trust who has used their services. Because of the high demand for immigration into the United States, there are many unscrupulous people involved in such matters.