Can oil that we drink, lubricate bile ducts?
Not the way it can lubricate our mouth. (as most people may imagine a picture of oil passing through bile ducts and lubricating bile ducts that way, what is incorrect)
Oil will never reach bile ducts, not in the form of oil.
It may reach bile ducts in the form of cholesterol acids, in some future.
Oil that we ate last few weeks, may have been absorbed, may have been used for creating cholesterol, and that cholesterol have been broken down into bile acids that bile is composed of, and that bile will lubricate bile ducts, or it will be used to create more cholesterol stones.
Every drop of oil that we get into our mouth and that we swallow, sends message to liver to produce appropriate amount of bile.
When that bile is produced, it moves through intrahepatic bile ducts, toward gallbladder, and it lubricates bile ducts.
When it reaches cystic duct, gallbladder do its best in an attempt to suck it in, and if it get sucked into gallbladder, in that way it lubricates cystic duct and gallbladder.
When oil reaches duodenum, few hours later, bile is emptied from gallbladder and from liver bile ducts, and that bile then lubricates the common bile duct and duodenum, and then the rest of GI tract.
So, while it is not correct to say that oil will lubricate bile ducts, (as most people may imagine a picture of oil passing through bile ducts and lubricating bile ducts that way, what is incorrect), it will actually happened!
Bile ducts will be lubricated as a consequence of consuming oil.