Portugal Spain trip in April

Cordoba for me is definitely worth more than a stop en route - at least one night, preferably two.
Unless you have a particular reason to visit Lagos, I wouldn't bother.
Otherwise, looks fine to me.

With only 1 night for Granada and a stop en route to it, that leaves you with only a partial day in Granada. With that short amount of time you may as well not go. If going to the Alhambra and Generalife, that could take a half day or more to visit and you haven’t allotted enough time.

If I’m reading the itinerary correctly you’re picking up a vehicle in Lisbon and dropping it in Lagos, or continuing with the vehicle on to Sevilla. There will be a huge, possibly €500 or more to pick up the car in Portugal and drop it in Spain.

It’s not my trip, but if it was I’d drop Granada and Lagos since you’re severely limited with the time you’ll have in both places. Either that or drop one of them and add the day to the other so you have a full day in either Lagos or Granada.

If the trip is over Easter, be aware that lodging prices in Sevilla will be elevated due to the popularity of the Semana Santa activities.

You say that you don't want to be rushed, but your itinerary is very rushed.

You only have 1.5 days in Porto and Lisbon, perhaps you should consider skipping Portugal this time.
Last time I was in Portugal is was for two weeks. You didn't include visiting the amazing Douro River Valley, which is one of the most scenic river valleys in Europe.
If you do go to Porto, consider taking a cruise up the river, or take a train up the river to Pinhao and Regua. The train tracks run along the north side of the river.

How will you go from Lagos to Seville? Do some research, I think train connections may be difficult. IF you rented a car and dropped in Spain there would be a huge drop charge.

You didn't mention visiting two wonderful cities just outside Madrid, that being Toledo and Segovia. Don't miss them.

Not sure you will have much time in Granada or Cordoba, better do some research and plan your transport.

There are no trains between Lagos and Seville. There is bus service from Faro to Seville. The other posters are correct in pointing out the likely very high international-drop surcharge if you return a Portuguese rental car in Spain. Unfortunately, Portugal and Spain are not well connected by public transportation. With as little time as you have and a desire to cover Spain from Seville all the way to Barcelona, I'd postpone Portugal until you can give it more time. This would also allow you more time in Spain.

You do need more time in Granada or it's simply not worth going. Better to use that day to see Cordoba.

There are quite a few trains per day connecting Granada and Madrid. Two of them take less than four hours. I'd prefer one of those trains to a flight.

I agree: I would skip Portugal on this trip. You have allotted far too little time for the Andaluz cities.

Compare the cost of the car drop-off to the cost of hiring a driver for that leg of the trip; might be cheaper to get a driver.

Me, I'd also skip either Barcelona or Madrid, and spend that total time in either one of those cities; you do not have time to see both in 4-plus days.

There will be no time to chill with this agenda. You absolutely need to cut a few places.

Day 6 leaves you will a lot of driving, finding parking, with little time to see Lagos. And the next day, a three-hour drive to Sevilla with only two full days in that city...not good. Skip Lagos.