I know it's not what you asked, but it's relevant, OP.
I would be more disappointed in myself today than my DS if I were you, that he has got to the age of 11 and can't swim. And as for the punishments you've dished out...!
It doesn't excuse it, but he felt driven to lie through a double whammy of peer pressure & humiliation, I expect. No one wants to be the only child who can't swim in that situation.
Two of my 4 DCs have told lies to cover their tracks when they have put themselves in potential danger. They all know that lying to me is a line they shouldn't ever cross, but they did it nonetheless.
There were no punishments (arbitary or otherwise) & no raised voices, yet I actually think I couldn't have handled those situations any better than I did. I made a point of staying calm, & tried to empathise whilst not excusing the behaviour or lies.
We talked it through till the cows came home. I can not control whether or not my kids lie to me in the future, I can only try and guide them to make the right choices, and just as importantly, make it known that if they mess up and lie again, I will be pissed off & disappointed , but that I'lll get over it & that they can still come to me & tell me, or phone me if they need me, and I will support them as best as I can.
All that you might have achieved as a result of this is that in future, he tries to cover his tracks more successfully. I hope I'm wrong, though.
As he moves through high school, he will need to be treated less like a little kid, and more like a young person who you can reason with.
I would give him a big hug, tell him you understand how hard it is to be the odd one out, apologise for getting him to age 11 and being unable to swim, but discuss what he could do when he finds himself in a similar situation in future (not water based, but in general), and how sometimes he needs to stand his ground, but that you get that at other times, you appreciate that this seems too difficult. Come up with a plan:
Eg...Oh, I've got a missed call from my mum...I'm just gonna call her back...he could call you, say sorry I missed your call, which could be your mutual cue for you to pick him up & ask questions later, meanwhile, he could say to his mates - I've got a doctor's appointment that mum forgot to tell me about, so she's coming to get me, I'll have to go (or some other reason).
I think the writing punishment & gaming ban will just make him resent you & potentially be more sneaky.