I suppose Liz was able to be cooler and more in control with Burke because it wasn't her secret, she didn't know it, and she didn't feel vulnerable. If she, say, disoriented Jason and took wind out of his sails by entertaining him and serving tea, say, it might help, but this issue is her one vulnerable spot. Anxiety goes up, using brainpower that might otherwise be put into crafting devious counter-tactics.
How can someone be SO comfortable in a place where he's definitely not wanted? Jason manages it. First unappearance of a new regular character, on the other end of a non-existant phone call made by Jason, involving no actual actor. When the actor does appear, it won't be the one we know and love. It'll take awhile, but good our old [spoiler]Willie Loomis[/spoiler] will arrive... bit by bit!