I have a 88 sport coupe and i want to put a fun exaust on it including a set of headers my question is what are the lines that run into the exaust manifolds and how easy are they to dispose of??

 

The lines going into the exhaust manifolds (and one goes to the catalytic converter) are the Air Injection Reaction (aka, A.I.R.) system.

They aren't hard to dispose of unless you have emissions equipment inspection in your area. In that case, they may be impossible to dispose of.