Here is his 2009 line :
.175 / .283 / .223 in 124 PAs
2008 wasn't that bad, and 2007 was actually alright but combined they only accounted for 51 PAs. If we take a look at his minor league splits, we see the same issue
2008: .244 / .293 / .267 (86+ PAs)
2007: .286 / .344 / .314 (35+ PAs)
Two things jump out. He didn't hit AAA lefties well AND he didn't face many of them. (and my god, that lack of power...) We have to assume with those PA #s that not only did Morgan not face the good lefties, he probably didn't face many of the just ok ones. What will he do against major league lefties? Well I think we saw that last year.
God bless him he wants to hit lefties, which would be fine if Morgan was a 22/23 yr old who just needs to see southpaws more to get them down. Morgan is a lot of things, but young ain't one of them. At 29 going on 30 we can't expect any great changes in what we see (and let's face it, Morgan is making the basic optimist mistake of assuming all the good things - in this case his rockin' of righties - will stay the same and if he just improves the negatives he'll be great. He could easily see a return to normal against righties.)
So what's the answer? Farid over at Bleacher Report proposes a Maxwell/Morgan platoon. Problem with that is relying on Maxwell to hold up his end of the bargain. His line last year was .242 / .342 / .273 against lefties in the majors, .245 / .372 / .330 against them in the minors. At 26 this year, do you really want to go ahead with this as Plan A? Sure you'd likely get some boost in average and OBP, Morgan is that bad, but not that much. Plus what would you be losing in fielding? To me there are too many questions to platoon. The other option off the top of the head is Willie Harris, but he's just like Morgan: .121 / .356 / .212 last year vs lefties, and history suggests not much better than Nyjer.
A more radical choice would be to use Mike Morse. Morse can't play center but if you put him in right and move over Dukes to center you could have a very good lineup vs lefties... and possibly the worst fielding outfield in the majors.
The truth is there is no good answer, not in the Nats camp right now. Given Morgan's insistence that playing time is what he needed to get hot, and his fielding which is not dependent on the handedness of the opposing pitcher (at least not until they come up with a stat for that) the Nats are probably better off doing nothing. Outside of the Phillies, the NL East is pretty righty heavy with only 3 (maybe) lefties out of 15 starters. I say suck it up - let Morgan play full time.