What is the best way to travel from Lagos to Evora??

A) In summer (July 1st to the 15th of September) there are two direct Rede-Expressos coaches from Lagos to Evora at 12:15 and 15:30 every day. The trip takes about 4hrs 15 minutes and will cost €17,80 each.

B) Outside that period the only direct service is on Sundays at 17:00hrs. Details at www.rede-expressos.pt
tickets can be bought on line up to 15 days before travel.

C) By train it is quicker, but only two possible trips each day, leaving Lagos at 06:14 and 14:00. That takes 4hrs 10 minutes, two changes of train are involved and that will cost €33.

Rome2Rio.com is a good starting point for answering questions like that. I write "starting point" because you simply can't trust many of the details you'll see on the initial result screen. The fares and travel times are not reliable. One level down you'll see frequencies, and you can't trust those either. But you can keep clicking though the website and eventually find the name of the bus and rail companies that are options, and there will be links to websites that often (not always) have schedules.

Occasionally there's bus service Rome2Rio doesn't know about, but I've found the website is generally accurate as to what types of transportation are available (though possibly not on weekends or holidays) and where you may need to transfer.

In this case a bus seems more direct and faster. Probably also cheaper. Rede Expressos is the company providing bus service.

Here's a link to the Portuguese rail website.