Culturally speaking they're more similar than most other countries in the Middle East, yes.

They're really quite similar but there are big differences. I can only explain in stereotypes

Ethnically they're quite similar, but not exactly the same. The vast majority of Palestinians are at least partially (if not fully) of Jewish origin, with Assyrian, Aramean, Greek, Roman, Turkish, and Arab mixtures. Lebanese and Syrians are mostly of Canaanite stock, with most Lebanese historically speaking the Phoenician language and being of that background while most Syrians are closer to Mesopotamian Assyrians (though not exactly the same) and Arameans, but both also have some amount of Jewish, Greek, Roman, Persian, Turkish and Arab mixture. Jordanians are similar, but are more likely to have a bit more Arab mixture in their ethnic composition.

Culturally they are quite similar but different because of the religious compositions of the country and the geographical landscapes. For example, Lebanese are historically a Maronite Christian/Druze population with a Sunni and Shia minority (also most other Christian denominations and Jews) with a French colonial past. Even though in the past 35-40 years Muslims have become the majority, the culture is not very Muslim or Arabic compared to others in the region and has a big French influence too. The fact that they are a coastal and mountain people also influences their culture. Syrians are similar though the land's diversity and more Muslim population (though still with a big Christian and Druze population) has a different feel. Jordan's population is far more Muslim than any of the other countries but British colonisation is also felt there, though it is definitely more conservative than Lebanon and Syria. Palestinians seem to be more "villagey" though there are also coastal and urban people too. They are about 70% Muslim and some are very religious, but Christians have a big part in their society too so that balances it a bit.

I would say Lebanese are more culturally similar to Greeks, Italians and other Mediterranean people. Syrians are a bit more close to other Middle Eastern countries but still Mediterranean. Jordanians are a bit more urban and Palestinians are more varied.