Washington certainly has the rotation depth to make such a move. Barring injury or trade, they'll likely break camp with six starting pitchers on the active roster: Lannan, Stephen Strasburg, Gio Gonzalez, Edwin Jackson, Jordan Zimmermann, and Chien-Ming Wang.
As for Lannan's allure on the market (besides the general interest that surrounds any starting pitcher up for trade), the Nats will no doubt find suitors. Lannan will be arbitration-eligible for the third time after the upcoming season and is slated for free agency following the 2013 campaign.
In 2011, Lannan posted a 3.70 ERA in 184.2 innings. However, Lannan's peripherals (i.e., things like strikeouts, walks, and home run rates) suggest he was a bit lucky last season. Most of the projection systems tab him for a 2012 ERA that ranges from slightly better than league average to slightly worse than league average. Still, a guy who can give you average-ish innings from the back end has value. Since the Nats will be dealing from a position of strength, trading Lannan makes sense.
On the other hand, almost no team uses just five starters for an entire season, and given Strasburg's probable innings limit and Wang's injury history (and the Nats' legitimate designs on contention), depth might be more necessity than luxury for D.C.