Lloyd is heading from the Houston Dash to her home state of New Jersey to join Sky Blue FC in the three-team trade, which saw the Chicago Red Stars acquire Kerr from Sky Blue and Houston add Press from Chicago.
Lloyd, 35, scored seven goals in 15 games while spending the past two seasons with Houston. She also spent the first half of 2017 on loan to Manchester City.
A 24-year-old Australia international, Kerr scored 17 goals last season while claiming the NWSL Golden Boot in addition to MVP honors.
The 29-year-old Press scored 35 goals over the past four seasons with Chicago.