Spain/Portugal/Gibraltar - Madrid to Lisbon and Lisbon to Madrid

I have a question regarding flying to Lisbon from Madrid and then back to Madrid........how involved is customs to go through and how much time should I allow. When we return from Lisbon to Madrid we want to catch a train to Cordoba.
Question: How much time to allow going through customs and......also can we just find a train that day or should we make train reservations to go to Cordoba?

No customs at all if you are travelling between two airports within the EU/EEA as these are.
As both countries are also in the Schengen area, no passport controls either (though the airline will want to see passports at checkin and/or the gate as proof of identity.

When we return from Lisbon to Madrid we want to catch a train to Cordoba.
Question: How much time to allow going through customs and......also can we just find a train that day or should we make train reservations to go to Cordoba?

You can find RENFE tickets at a discount when purchasing in advance, but those tickets have more restrictions on changes and refunds... Just check out the discount availability for the trains that you may want and see. I don't know how full trains are on that route, but getting the tickets in advance will get you a spot on the train and you could get a significant discount.

I would book train reservations in advance to go to Cordoba - use www.renfe.es rather than RailEurope or one of the other rip-off merchants. It may not sell out, but the online fare is €27.50 vs a walk-up fare of €68.40.

Expect a 40 mins to get your bags at LIS when you arrive. If you're flying TAP, you need to have your bags checked at LIS 60 mins prior to departure. For other airlines it's probably less. The airport itself is easy to get through. Plan on having it take 60-70 minutes between MAD and Atocha. Also, consider flying LIS-SVQ and taking the train from there. It will probably be more expensive, but you'll save about two hours doing that, or you can see SVQ before heading to Córdoba.

You can consider driving from Madrid to Lisbon;
when you add the travel to the airport, check-in, wait, flight, arrival at the other end and getting to your hotel, door-to-door travel can be as much as 6-8 hours (or more if there are delays).
The road trip is actually nice, highways are great and allows you to stop along the way; you really do not need a car in Madrid, but a car in Lisbon may come in handy to do some out of town trips
Not sure what is your itinerary, days available or interests.
As long as you pick up and return to the same location, cars are not very expensive in Europe. Gas is pricey, some tolls are costly but cars are smaller than in the US and more gas-efficient.

You can consider driving from Madrid to Lisbon;
when you add the travel to the airport, check-in, wait, flight, arrival at the other end and getting to your hotel, door-to-door travel can be as much as 6-8 hours (or more if there are delays).
The road trip is actually nice, highways are great and allows you to stop along the way; you really do not need a car in Madrid, but a car in Lisbon may come in handy to do some out of town trips
Not sure what is your itinerary, days available or interests.
As long as you pick up and return to the same location, cars are not very expensive in Europe. Gas is pricey, some tolls are costly but cars are smaller than in the US and more gas-efficient.

One way drops are horrendous, so unless you're planning on returning the car to MAD, it's not worth it. Return fares can be had for as little as $50 in IB

One way drops are horrendous, so unless you're planning on returning the car to MAD, it's not worth it. Return fares can be had for as little as $50 in IB

my previous post says specifically that if you pick up and drop off in the same location prices are reasonable.
I assume the $50 is without taxes; once you add fees, taxes, cabs to the airport it may not be a bad idea to rent.
The poster just says we so it is at least 2 people traveling.

my previous post says specifically that if you pick up and drop off in the same location prices are reasonable.
I assume the $50 is without taxes; once you add fees, taxes, cabs to the airport it may not be a bad idea to rent.
The poster just says we so it is at least 2 people traveling.

$50 (36€) is with taxes, return ticket on promotion fares that IB has quite often. The cheapest at the moment is 40€ ($59) return fare on AirEuropa (UX). Metro to MAD is 2€, bus from LIS to the center is 0,90€. Parking in LIS city center is horrible, but the car is useful for trips outside of LIS area.