If LAX-TYO (I presume HND?) is on DL, yes, DL will check through-check your bag across both tickets. Have a printout of both tickets and present both tickets at check-in at ATL. Ensure the bag tag shows “HND” before the agent places the bag on the belt to send back.

Note: upon arrival at LAX you may receive notifications of “Welcome to LAX. Your bag will be arriving at Claim X.” If your bay was tagged properly you can ignore this as your bag will be transferred to the LAX-HND flight.