"I have no problem with World Cup games because they are on set international dates," Lawrence told the Echo.
"We will swallow the travelling because we support our players turning out for their countries.
"But Concacaf Gold Cup fixtures may be a problem. We will look into exactly when the matches are, but I will be talking to Jamaican officials."
Lennie is concerned after seeing both Alan Lee and Graham Kavanagh crocked while away on friendly duty for their home countries.