That's a really good question. I highly doubt it. It wouldn't work either.
If you can afford an LS and you wanted the looks and the performance, you would get yourself an LS F.
No. The F-Sport has never been about performance. It's for people who just want sporty
looks and
handling but not performance.
I think an F-Sport version won't come to the LC and the LS because:
1. Looks-wise, what immediately sets the F-Sport apart from the regular versions have always been that the regular versions have horizontal slats in the grilles, while the F-Sport versions have mesh grilles. Now that the regular LC and LS have mesh grilles to begin with, there's no more easily noticeable feature to tell the F-Sport apart. The regular LC and LS also both look sporty and menacing just like an F-Sport should already--the regular 5LS actually looks way more menacing than the 4LS Sport IMHO.
2. Handling-wise, the all-new GA-L platform is so rigid and sporty to begin with, it makes the "regular" LC and LS handle so well that there's no point of a sport package. Heck, they both even come with rear-wheel steering standard! The 4LS didn't handle nearly as well, so the Sport version (short of calling it the F-Sport) did make a meaningful difference to those who care.
In short, there's absolutely no point of an F-Sport version for either the LC or the LS when the regular versions of both already look and handle the part.