Hi I will fly from Porto to Seville; would it be best to rent a car in Seville to drive back to Lagos or would it be best to take another form of transportation to Lagos and rent a car there to drive back to Lisbon?
The biggest issue with renting a car is that you would be doing a one way international drop-off, price it, but it will be costly.
Otherwise, by public transport, there are no trains, but you can take a bus from Seville to Faro (or to Tavira) and take a Train or rental car to Lisbon from there.
Look in to daytrip.com we are doing the same Seville to Faro. I booked a van for 4 adults the cost is $341