Can I use a part of a ticket?
 

I am looking at flights to Dubrovnik and found a flight on LOT airlines that flies from ORD to Warsaw to Dubrovnik. But there is another flight that flies from ORD to Warsaw to Munich that is much cheaper. Could I check my bags thru Warsaw and not use the Munich portion and buy another ticket from Warsaw to Dubrovnik?

Yes but (1) you would need a long layover in WAW to convince the agent to short check your bags and (2) you would forfeit the return part of your ticket.

EDIT: and (3) if WAW-MUC and WAW-DBV are with the same airline they might pick up on that and cancel either flight or both.

LO most will run so called horizontal and vertical duplicate checks to ensure their revenue integrity is not hurt, so you may get a call asking what you are up to. Also the agent in ORD is very unlikely to short check your bags. The only way you could mitigate this is by booking a significanly long layover in WAW, like 15-20 hours.

without checked luggage.....
otherwise I would do a consultation at the airports doc...., so much headache, isn't ist?