Will be arriving from Budapest. Do I go though passport control again and if so how long does in take on average?
You won't go through passport control in Lisbon as Hungary and Portugal are in the Schengen zone. This the equivalent of a domestic flight in the USA,
Will be leaving to fly back to the US, what are the steps (check-in, passport control, ect.) and average time to go through it all?
You will go through passport control on your way back to the USA.
Just start the entire process 3 hours before the flight; that is the the standard. Not unless the airline contacts you to say otherwise, which they will do the day before the flight.
Edit: Sometimes there is a 2nd security screening after the 1st one when flying back to the USA and this is what takes up a lot of time.