Starting in v1.60, we can send tweets from inside LO2.
Here's how you do it.
Type some text into a headline.
You can see how long the text will be by watching the attribute list below the outline display. There's a new length readout that tells you how long your headline is. If you plan to tweet it, don't let that number over 140.
When you're ready to send the tweet, click on the Twitter icon in the left margin. You'll get a confirmation dialog, to be sure you didn't click the icon by accident. Click OK to send the tweet.
If you want to see the tweet, click the Twitter icon again. You can also get there by double-clicking on the headline as if to expand it. If it has no subs you'll be taken to the tweet on the Twitter website.
If a headline has a url attribute, it will be added to the end of the tweet before sending. Make sure there's an extra 25 characters for the link when you're editing the text of the tweet. If there isn't room you'll get an error dialog telling you how many characters there were.
To add the url attribute, click on the suitcase icon in the left margin. This opens the Edit Attributes dialog. Click the + button to add a row. In the left column of the newly-created row enter url, in the right column the url itself, and then click OK. Here's a screen shot that illustrates.