I hope you are enjoying your stay at LIS
I don't know where in the city you are staying, but LuisG is right, your best bet is the nº 17 Bus. It leaves from Praça do Chile, subway station 'Arroios' (green line), every 15 mins or so. Either that, or take a cab from 'Campo Grande' subway station.
In any case, you'll want to get to 'Calvanas' neighborhood on the road to 'Camarate'. After 'segunda circular', heading towards 'camarate', it's the first houses on your right, there's a small street where they are demolishing houses. That's for the threshold of 03. Or ask the driver for 'transportadora lusitania', a transport company located at the intersection, some 2 more kms down the road.
The threshold is good for when runway 03 is in use, but if 21 is being used like today, the intersection is a much better place.
If you need additional info, or maps or something, feel free to email me. My contact is on my profile. And if you are around Saturday, let me know, I'll be at the airport also, and I can show you around.
EDIT: I've found this link from a fellow spotter: http://www.miguelclaudio.com/lisboa.htm
. The locations I refered were nº 1 and 2. Dont' go to locations nº 3 or 4 alone, as security is a concern at those sites. Location 5 is great in the morning, but you'll miss departing traffic, and sometimes you are questioned by the local cops.
[Edited 2005-03-15 13:05:30]