I've tasted Turkish Delight.
I've played the Moonlight Sonata.
I've danced a tarantella.

I suppose all of these are plausible.
I tasted Turkish delight, so why not you? Besides, I think that you'd probably think of this because you have tasted Turkish Delight, rather than randomly trying to think up something.
I know you played piano. . . So it seems plausible that you've played the Moonlight Sonata.
But a tarantella seems somewhat random -- why think of this if you hadn't danced one? A little research shows it to be a Mediterranean (Italian?) dance, quick and lively. When my wife inquired of me about what I was watching, I indicated it was a tarantella and she responded something to the effect of, "I played one of those on the piano."
I think you thought of the tarantella because you've played one on piano.

So I do not think you've danced a tarantella.

No, I haven't. I'm short on lies.

I have eaten elk.
I have eaten octopus.
I have eaten frog.

I'm gonna go with octopus.

I realize I have made an error, so I will give you this one. I should have said "squid" and not octopus. Calamari I think is technically squid, which is what I have eaten.
I have eaten elk, but never frog.

I've worn tight pants.
I've ridden in a tight car.
I've gotten stuck in a tight gap.

I think we've all worn tight pants when we're growing up and start to outgrow them.
Also, no doubt we've all ridden in a tight car.
Then again, getting stuck is not so uncommon, but I'm going to say that you've not gotten stuck in a tight gap.

Yeah, that's it. That was simple.

I have battled atop a frozen lake.
I have been routed by the touch of a leaf.
I keep a sword in my office.

I'm gonna say you don't keep a sword in your office, since I'm not sure that's even allowed anywhere. I was going to go with the leaf, but it sounds plausible, and I can see you staging a fight on a frozen lake. Somehow, though, I'll bet I'm wrong.

Well, you got it but not for a reason I'd considered. My office is in my home, and currently there is a bow on the wall and it didn't occur that you may have thought my office was outside the home.

I spotted a sneak attack and charged with my compatriots against the foemen and met in snowy battle on a starlit night atop a frozen lake in the north woods. Fortunately, the battle was waged with white washing and wrestling and such like, and it ended in good spirits.

When first I wandered into a patch of stinging nettles, it resulted in a quick flight to reach the Belle River in hopes of gaining some relief by entering the muddy water.

I've gotten lost in the supermarket.
I've wandered many a backroad of the hometown.
I've been to Chicago.

I'm guessing you haven't been to Chicago.

Yeah. Sister's been there, I think, but I've barely been out of state. Don't really care to leave.

I wish I had a more complicated lie than that.