And if a skater was completely able to jump in both directions we could see triple lutz/triple lutz combos which would be very cool.
I don't think it is possible. I remember reading on a different forum that a coach wanted one of his (low level) skaters to include Lz-Lz combination in their LP, but when he consulted the judges, he was told that it is not allowed.
It would be cool to see something like this in an exhibition, though.