Leadership Institute for Transatlantic Engagement Act or the LITE Act This bill establishes the Leadership Institute for Transatlantic Engagement to develop a diverse community of transatlantic leaders at all levels of government who are committed to democratic institutions. The institute shall award grants for entities and individuals in the United States and abroad to assist in the institute's work conducting research, international exchanges, education, and outreach to strengthen (1) democratic institutions, including civil and human rights; (2) emerging and current political leaders and their employees; and (3) interest and excellence in international public service careers. The institute may develop such programs, activities, and services as it considers appropriate to (1) increase awareness of the importance of public service careers that focus on international affairs and civil and human rights, (2) provide training and development opportunities for domestic and international elected officials in performing their public duties, and (3) enable transatlantic political leaders to gain firsthand exposure to U.S. democratic institutions through visits to the United States.