I don't know what word you could use for being forced to lie, but I frequently use one for what you have to do when you're in that difficult situation. I call it "pre-truthing". Say, for example, someone invites you to come and look at their 5,000 vacation pictures on Friday night. You know you have no obligations, but you quickly say "I'm going out with a friend that night, sorry". Then you phone all of your friends until you find one that will go out with you, thereby making your statement retroactively true.