Your (reasonable) public transport choices are:
1. Take the day bus (7-8 hrs)
2. Take the overnight bus (same amount of time, you get in around 7-8AM)
3. Take the AVE to Madrid and fly to LIS. This should be a bit faster and maybe cheaper than the buses.
4. Fly to Madrid and then to LIS. Ryanair has good deals on the flights to Madrid (I'm sure the competition does too) and there are enough cheap flights between LIS and MAD. Look into RT flights as those tend to sometimes be cheaper than OW flights on legacies (IB, TP). Easyjet and AirEuropa also operate on this route.
Portugal's motorways have tolls on them, so consider that and the fuel prices when you decide on renting a car. No way to avoid one-way fees that I know of.