If you're tweeting from the outline, you can have LO2 automatically check, every three minutes, if there are replies to any of your tweets.
To turn it on, visit the Settings dialog in the System menu.
In the Tweets tab, there's a new checkbox. Click it and click OK.
That's it. Now every three minutes LO2 will ask Twitter for any replies and insert them beneath the tweet they are in response to.
Current replies are shown in green, i.e. if they were found the last time we looked. So they stand out a bit. The green is gone the next time we search.
It only checks the outline in the current tab and it only checks if the outline has tweets. You should put all your tweets in one outline. If you put them in more than one you will lose replies. If you don't care about replies, you can put them anywhere.
This feature is available in LO2 v1.61a.