Equal Justice for Immigrants Act of 2019 This bill contains various provisions designed to protect migrants, such as limits on deportation. An alien arriving by land to the United States seeking admission may not be returned to the last country that the alien was in while immigration proceedings are pending, unless the alien affirmatively consents. For an asylum seeker who is a member of a vulnerable population, the Department of Homeland Security shall ensure that the number of interviews required is not overly burdensome. The Department of Justice (DOJ) may not impose production quotas or other time-based metrics on immigration judges or use such metrics to evaluate a judge's performance. The government may pay for counsel to represent aliens in various immigration proceedings. For indigent aliens, the government shall appoint counsel. An alien eligible for a removal proceeding may not be removed prior to the date of such a proceeding. The bill extends to 60 days the deadline seeking review of a final order of removal, and authorizes the court to extend that deadline an additional 30 days in certain instances. A petition for review shall stay the removal. After the Board of Immigration Appeals affirms a removal order, the DOJ shall provide the alien a written notice of the alien's right to appeal the decision and certain information related to such an appeal.