They are new. Never opened. Sealed. Do I have to bother sterilizing both lid and bottle by immersing them separately in canner and pan? Or are they safe and sterile considering they are straight from factory?
You should sterilize your jars and lids before every use.
The dust that gets on them between uses and even in the box is enough to warrant sterilizing.
It doesn't take long. Running them through a cycle in the dishwasher with a steam or sterilization step is enough. I boil the lids in a small sauce pan.
Debbie M's comment below made me think that some clarification is warranted.
Lids used to need to be heated to soften the seal so it would seal properly. That is no longer the case.
Additionally, bottles and lids don't need to be sterilized if they are going to be processed for longer than 10 minutes or pressure canned.
Foods that are processed less should have sterilized jars and lids. I am in the habit of washing them in the dishwasher which also sterilizes them.
The current recommendation of the company that owns both the Ball & Kerr brands are that it is only necessary to clean the lids, bands, and jars well with soap and water before canning with them (a normal dishwasher cycle is fine). The canning process itself will sterilize them. It is also no longer necessary to heat the lids to soften the plastisol gasket.
Used jars should be sterilized and carefully checked for chips or cracks. Used lids should be discarded, or used for purposes other than canning (keeping jars in the refrigerator, or vacuum sealing dry goods, for example). Used bands should be cleaned.