I've been on this tour!  It can be really independent, but if you do all the optional excursions, you wouldn't have too much free time at all.  It really depends on your preferences and how comfortable you feel exploring on your own.

I think any time would be great to go to Lisbon!  The city is beautiful and the weather is great.  I went in February (when the prices are lower!) and our weather was in the 60s and 70s every day - much better than it was in New England.

My favorite excursion was the West Coast, a full day excursion that includes a white-washed walled town, the beachside resort town, a huge monastery and the major pilgrimage destination of Fatima.  I tend to be a pretty independent traveler, but there was no way I would have been able to see those three towns on my own.  The included lunch was great, too, in an airy restaurant overlooking the beach.

Another good thing to consider is that even though Portugal is on the euro, things tend to be much less expensive than in places like France and Italy.  We could get a very filling lunch of sandwich, pastry and beer for around 5-6 euros.