The Dallas Morning News first reported the pending ban.
Lawrence was previously hit with a four-game fine for a substance abuse violation, making a four-game suspension the next step.
Dallas already had huge question marks along the defensive front entering next week's NFL draft. Earlier this offseason, defensive end Randy Gregory was suspended for the first four contests for violating the NFL Policy and Program for Substances of Abuse. The Cowboys have wanted nothing to do with bringing back Greg Hardy. Jeremy Mincey also remains unsigned.