I am having difficulty using on-line services to arrange car rental in southern Spain and returning it in Lisbon a week later. Should I expect a huge fee for dropping the car off in another country? I will be traveling in late September and staying near Gibraltar. I would appreciate your suggestions.

Yes, expect a big drop charge.
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ditto, Bob

Check with a bunch of agencies. Expect all to have a drop-off charge. It may differ by agency and by type/class of car you rent.

We did it the other way around once - rented in Lisbon, toured through Spain and returned to Madrid with no drop off charge - since we were returning a Spanish car to Spain. But I think this is much less likely th eother way around.

What nytraveler did isn't something you can arrange in advance. I presume the rental company happened to have a Spanish car that needed returning, and could do a deal.
Your choice is really to do two separate rentals. One in Spain, then train, bus or fly to Lisbon and rent another.

I looked into this Spring.. and gave up on the idea. Pricing nearly killed me.

We wound up renting in Madrid, doing a large loop out of Spain, down Portugal and ending in Seville where we dropped the car. Much more reasonable.

If I hadn't wanted to do Seville I probably would have just tried flying from Madrid to Lisbon on Vueling and picking up there.

We rented in Lisbon and returned the car in Madrid. The dropoff fee was hundreds of dollars, but we were locked in to that itinerary. I would plan differently if I were in that situation again.

Ditto what others said about a big drop-off fee.

However, we had the same luck as nytraveler albeit in Germany. We need to fly out of Vienna and we rented the car in Munich. Luck was on our side, as they had a car with Austrian plates that needed to be returned in Austria, so no drop-off fee for us. It does happen once in a while.

It works more often if the countries are immediately adjacent - and the country has a lot o rentals. Portugal has many fewer tourists than Spain so the chances of picking up a Portugese care in Spain are probably pretty slim.