Yes, I think a toeless lutz would have to be done with the free leg behind, similar to a walley (or a lutz, haha). My thought is that when no toe pick is involved, then when rotating in the same direction as the entry edge, it's better to place the body (and hence the free leg) within the circle being made by the entry curve. Hence the salchow, loop, and inside axel positions; the axel being the exception because of the power of the free leg swing. But for counter-rotated jumps, it's better for the weight to be outside the circle, essentially because you're switching circles in the air. Hence the walley (and thus the toeless lutz) I'd expect the free leg to be behind.
It's just a bit of speculation though.
It's just a bit of speculation though.