The answer is it depends. What type of an operation you are talking about. How much of the capacity is being consumed. How long the process it takes to complete. How physically close the process is to line. You will have to learn how to handle shared equipment.
An example of a paint system. I recently toured a company where the paint system was located in a different building away from where the parts were manufactured and assembled. Additional time would be required just to transport the product but you also lose the quality tie between processes. Say a part is dropped and damaged at the paint system, is that communicated back to the supplying system to remake or repair the part. If the paint system is working at close to maximum capacity there would be challenges on which product to work on next.
Each operation implementing lean must review this sharing of resources and plan for the challenges.
I would agree with BillPSU that the answer to your question as stated is "it depends". FIFO may or may not be the way to go for any particular process. Forecast Batch procedures may work better in some cases as it can reduce the time spent on machine setups/changeovers. This is best done for mature parts or stable processes that behave in a consistent manner. Look at how a piece of equipment is utilized both on run to run terms and the long term.
