I'd guess there was a stash of clothing on the Falcon and Lando borrowed a set of threads since Han wouldn't need them anytime soon.

Better yet, maybe at some point before the carbon freezing Lando and Han underwent reconstructive surgery to look like the other. So, it's actually Lando who is frozen in carbonite, and Han escapes Cloud City with the others.

Maybe that's why it takes a year to rescue "Han" (Lando) from Jabba's Palace. "Lando" (Han) puts off the rescue as long as possible because he's still pissed off at the betrayal.

They undergo further reconstruction sometime before the meeting with Mon Mothma.

It was all a clever ruse by Lando to get some action with Leia, both before the freezing and after. That's the ultimate payback for losing the bet and the Falcon - get with the dude's girl.