There is not going to be any shortage of plastics in the medium term.
Shale oil and gas production in the US produces vast quantities of ethane as a byproduct. This ethane is cracked into ethylene, a feedstock for making plastic. There is an oversupply of the stuff.
The overabundance is a big part of why it's just not commercially viable to do much with recycled plastic. Places will practically give away the virgin material because they have to find someplace for it to go to keep producing other things.
The amount of oil used for plastics or lubricants is insignificant compared to the use of oil as energy. In the United States, lubricants use ~0.5% of all oil, and all industrial feedstock about 1%.
It means the oil is being used for its heat content when combusted. Such heat may be used directly or be converted to mechanical work in a heat engine.
We burn 80% of the oil we take out of the ground. Oil production could drop 80% and we would not have to change anything other than demand for burning it.
Shale oil and gas production in the US produces vast quantities of ethane as a byproduct. This ethane is cracked into ethylene, a feedstock for making plastic. There is an oversupply of the stuff.