DFW-MAD Arrives at T4S
MAD-FCO Departs from T4

Go through Immigration (deal with immigration) and then take the train all the way to T4, where you will find the T4 lounge upstairs (this is the one you will use for FCO and it is called Dali Lounge).

Other two lounges are at T4S International Departures (Velazquez Lounge) in front of the Starbucks and at T4S level 0, downstairs (Goya Lounge), where the flights to Canarias depart from.

You will find more info in this thread:

http://www.flyertalk.com/forum/ameri...solidated.html