Balls and boots are reportedly among items taken after vehicles transferring equipment to the team's Swope Soccer Village base were broken into, according to the BBC.
Lucas issued a statement on X titled "Statement on heist in transit of English national team equipment".
"Yesterday, officials in Kansas City learned that at some point between their over-the-road transport from Florida to their arrival at the training facility in Kansas City, goods belonging to the English national team were stolen from the team's transport vehicle," Lucas said in the statement.
"Public safety officials at the local, state and federal levels are working to trace where in the United States the items were seized and all individuals who may have been involved. Further information will be provided by authorities at a later time."
Thomas Tuchel's England are due to train at Swope Soccer Village for the first time at 5:00 pm (2200 GMT) on Saturday after transferring from their pre-tournament base in Florida.
They open their World Cup campaign against Croatia on Wednesday, before further games in Group L against Ghana and Panama.
