There is no train service currently operating between Lisbon and Badajoz.
There are several daily long distance bus lines departing from both Lisbon Sete Rios Bus Station and Lisbon Gare Oriente Bus Station.
http://www.intercentro.pt operate three daily services departing Lisbon at:
09:30
14:30
21:30
Transit time is 3hrs:15mins.
Note arrival time is local time and Spanish time is one hour ahead of Portuguese Time.
If you go to the bottom of the following page on Cubsur's site you will find information on other services.
http://thomasallen.home.sapo.pt/travel/001.htm
Tickets for International Services like these can only be purchased at the ticket offices up to 30 minutes prior to departure.
