This annoyed me too, and it doesn't seem the solution is entirely satisfying — we'll just have to hope that Twitter for Mac gets updated soon to be better compatible with Lion.
If you have "Swipe between pages" set to "Swipe left or right with three fingers" or "Swipe with two or three fingers", then left/right three-finger swipe gestures will work in Twitter.
If you have Mission Control & App Exposé set to "Swipe up/down with three fingers", then you can hold ⌥ Option to use up/down three-finger swipe gestures with Twitter. (I'm not sure why, but if you have these set to 4-finger swipes, it doesn't seem 3-finger swipes work at all in Twitter.)
Have you checked System Preferences? Go to System Preferences -> Trackpad -> More Gestures and look at the top option (swipe between pages). If it is off, turn it on.
Best Answer
This problem is a known issue and has been fixed in recent versions.
However, it is not specific to Reeder and seems to also affect Twitter and other apps.
To work around it, hold ⌥ Option and swipe using the same count of fingers that you have set for Mission Control in Trackpad preference pane: