Sporting was the club bankrolled by the Viscount of Alvalade and coaxed Benfica players across the capital by promising better facilities. Benfica prides itself as the people's club something encapsulated perfectly by fans helping to build Estadio da Luz in the 1950s.
It's about 1 3/4 miles between the two - how about a rather swift walk! Maybe just leave the Benfica game 5 mins from the end if you see that the score wont change, and you will be one the first to leave the stadium, jump on a taxi to Alvalade stadium which is not that far, just over a mile.