yes, I have, but I don't with people who know me well - even if they don't know about my SA, they know that I'm antisocial in ways and that there are a lot of things most people enjoy that I don't, and they expect me to be reluctant. To anyone who knows me well, I'll often make an excuse out of something that I actually want to do but is of no real importance what so ever and could easily be done some other time or not at all if I wanted... but for the most part, I just say no and leave it at that and if they push more, I say nope just don't want to.
With more casual acquaintances that don't know me very well, like team mates, friends of friends and so on, yeah, I lie to make it easier to seem polite whenever I turn down an invitation to do something I don't want to. I often just say I'm busy and don't say what my other plans are but try to have an excuse in mind in case they do ask, which they rarely do. A bit of helpful advice for being a better liar (wow that sounds bad!) would to be as vague and give as little information as possible when there's no reason not to because that way, you don't have to always fall back on the same excuses or come up with new ones which doing a lot of probably makes people suspicious unless you're good at it. Try to be honest when there's little rational reason not to be though. When my anxiety was much worse, I used to lie out of fear and it got out of control sometimes like when I was panicking. One thing that's sure to make you anxious is feeling like you have something to hide especially when you think people might figure out you're lying about something... so honesty is good, not just for ethical reasons but for your own personal well being. I'm not lecturing anyone though because I think everyone lies sometimes and that lying in certain circumstances is totally acceptable. Anyone who says they never lie at all is either lying to you or they only believe it because they lie to them selves. That's what I think anyway.