Will the Insurance Company Continue to Pay My Medical Bills After the Case Is Settled?

Yes, as long as your lump-sum settlement included liability for X diagnosis and any treatment that is reasonable and related to the X diagnosis, the Insurer will be responsible for it. However, the Insurer can dispute any treatment. If they do dispute treatment, you will simply need to file a claim and argue it in front of an Administrative Judge at the Department of Industrial Accidents.