I don't know of any Alaskan LNG project. The proposed projects will never be economical because of the competition in the Pacific Rim, especially from Australia which has cheaper gas. The only economical way of delivering Alaskan gas to the U.S. will be a 52-inch, 3,600-mile pipeline from the North Slope to Chicago. At a cost of over $ 15 billion, that won't be ready for another 10 years, and will deliver about 5.5 bcf/day. By then, the situation will be desperate.
Alaska already exports natural gas via LNG.  It's not alot but it is most certainly operational right now.  The LNG is currently purchased by Japan as they are the nearest consumer that could utilize it.  If there was a terminal in WA or OR, no doubt some or all of it would make it to the L48.

Having said that, the real future for Alaska natural gas still lies within the pipeline route and not by LNG for obvious capacity and security reasons.