E Visa Integrity Act of 2019 This bill imposes additional requirements to acquire an E visa (for an investor or trader who is a national of a foreign country with a treaty of commerce and navigation with the United States, or an Australian specialty worker). Specifically, if an alien became the national of a foreign country with a treaty of commerce and navigation with the United States through a financial investment in that foreign country, the alien must have been domiciled in that foreign country for a continuous period of at least three years at any point before applying for an E visa. The bill also requires an alien seeking an E-2 visa (investor) to invest a substantial and economically impactful amount of capital in the United States, where currently the statute only requires an investment of a substantial amount.