Is your 'same' Bitcoin returned after closing a channel?

If your bitcoin in your wallet and all of it’s past transactions are all traceable down to the mined block it originated from;
Let’s say you open a 10 mil sat Channel to someone for a year.
When the year is up, Do you get your EXACT bitcoin back + and then some for the sats you earned?

1.) When you dedicate the .10 BTC to a channel, does it get ‘washed’ and sent around the globe before someone else’s .10 BTC is later returned to you a year later when the channel closes to pay you back?

  • or -

2.) Being that a channel creates a ‘bar tab’ on a past block in history, and settles on that SAME exact block when the channel closes - this prevents the returned bitcoin from being ‘newly generated’ from elsewhere. Thus meaning you DO get your original coin back?

I would think this has been thought of already during initial conception of Lightning to prevent bitcoin laundering.

(Both seem to make sense - the second one more than the first)

If the 2nd, You would think this creates a ever-growing strain on all machines keeping up with the blockchain - not only having to keep up with current blocks being mined every 10 mins, but also constantly scanning tens of thousands of blocks back in time for changes made due to the possibility of closing channels at any given moment.