Wont dry heat desiccate them like they do to bed bugs and wont they die after being without a host for a period of time?
Then use a lice solution from CVS etc.
I agree cool temps will preserve them. I have seen insects come to life after 2 weeks in a freezer.
Dry heat is fine, but it must be 140 degrees for a few hours, but that kind of heat destroys and is not advisable for use on most man made objects.
The stuff at CVS etc. is nothing more than a shampoo with pesticides. It should work on the liner, but rinse thoroughly. My only concern is it may discolor the fabric so test a small area first before use.