You may discover Lisbon street by street and district by district but to have a complex view of the city you should have a look at it from the Tagus River. It is not a complicated task to accomplish as you can find plenty of agencies offering tours on the river.
Take a short cruise before sunset as the warm summer light colours the city in yellowish and pinkish shades. Belém Tower and the 25th of April Bridge, Jerónimos Monastery and the Christ the King monument, and other astonishing attractions of Lisbon will never be the same for you.
On average, the cruise lasts for 2-2.5 hours so that you have enough time to enjoy views of the city just before it plunges into twilight. For such a tour, you can expect to pay approximately 30-40€. The tours run all year round, two hours prior to the sunset, so check the exact departure hours on the websites of tour providers. Summer months are the best time as the tours start later in the evening and it's much warmer so you can enjoy the night outdoors.