You might need to replace some things, like the rear storage box.
The cowling should not matter, as it is integral with the seat. It is the cowling/storage box match that is critical.
I assume the LS box is different from the standard '81-'84 box? I really don't know, myself.
The only other area that might come into play is the front of the seat, but I don't know why that would be any different. The tanks were the same, just different paint.
At some point, I see a '81-'84 seat in my bikes' future. I already have both boxes and subframe. One of these days I'll have too much money in my checking account, and I'll "dial-up"
S. Meyer and order me up one of those brand new replicas!

Tell me that ain't a thing of beauty, and for only $245 as I type this!

But...
for only a little more...

$300 USD as I type this.

Or maybe I'll just have to get both!