Lebanon is a country where its culture is made up of many different religious sects and it is wise to respect the religious differences of the Lebanese population.
It is recommended to wear modest clothing when visiting religious sites (Churches, mosques, etc) and when visiting rural towns and villages.
Even in Beirut, some areas are more conservative than others; visitors should bear that in mind when exploring the city.
Overall, however, clothing considered 'western' is generally acceptable, so to hedge your bets, keep your dress modest. Bear in mind, however, that as open and western as Beirut is, this is not Europe; "topless" at any beach, whether private or public, is not recommended at all.
In Tripoli, especially in the old city, it is recommended that women dress conservatively. The same applies to most traditional "souks" in the country.
In general, Lebanese are accustomed to different lifestyles and some do not take offence easily, especially with matters related to dress.
The Lebanese are people accustomed to diversity and are therefore quicker to accept different lifestyles, though not all Lebanese are so open-minded.
Because of political tensions and the conflict with Israel and tension with Syria, tourists should definitely avoid discussing politics, especially regarding these two countries.
Lebanese people, in general, are extremely hospitable and consider it an honour to have guests in their home.