At present there are only two airlines operating between Lisbon and Brussels.
TAP Air Portugal- http://www.flytap.com/Portugal/pt/Homepage
Brussels Airlines - http://www.brusselsairlines.com/com/
You may be lucky and be able to book a reasonably priced flight with either of the two given the time of year you wish to travel.
However, the cheapest way may be to take an early morning trains from Lisbon to Porto, get the metro to the airport and take the Ryanair.com flight from Porto to Charleroi in Belgium. Ryanair call this airport Brussels Charleroi but it is 60km from Brussels. However, there are buses from Charleroi Airport to Brussels.
There is a flight as follows:
Wed, 10 Fev 10
Flight FR 1387
11:30 Departs Porto
14:50 Arrives Charleroi
At present, the price is shown as 14,99 EUR.
BUT!! remember with Ryanair you have to pay for your luggage, credit card use etc.
As regards a train there is an 06:09 train from Lisbon Gare Oriente arriving in Porto at 08:44. This should give you enough time to get the Metro to the Airport. The ticket price will be in the order of 30.00 EUR.
You need to check the total cost of this option against the price of a direct flight to Lisbon.
I should also add that while long distance bus or train are an option, they will take over 24 hours and are likely to be as expensive or more expensive than the ryanair option mentioned above.
