Thanks for all the insights everyone. I really appreciate them.

So it seems like it is possible to make the connection, assuming that the Lisbon flight isn't delayed.

I'm actually asking this question for a friend who's interested in seeing Madrid for 24 hours but wouldn't be upset if she makes her connection and misses Madrid. I personally just did this connection 3 weeks ago and was able to do it in about 30-40 mins, but that's during peak season, and I was sitting upfront on the plane. Assuming her Lisbon flight is delayed or if she legit can't make the connection in 55 mins, how accommodating would Iberia be to rebook her on an Iberia flight leaving the next day? She wouldn't ask for a hotel or anything.

Would Iberia rebook me to a flight on the next day? I won't ask for a hotel or anything. How accommodating is Iberia? I won't check my bags, and I will be traveling solo. Both segments are on IB metal (but AA flight number). The flight on the next day is on a Tuesday in February to Chicago, so I doubt that the load would be high.