In the Lindström–Gessel–Viennot lemma (LGV) the lattice paths are taken to move in unit spatial-steps in unit time.

However, there are applications (here) where a version of LGV still "applies"(i.e. the LGV is used as an analogy) even though the paths are jumping in varying non-unit positive increments at each unit step time. In other words, a lattice path might jump two positive integers at time t: $P(t+1)-P(t)=2$ and three positive integers at some other time s: $P(s+1)-P(s)=3$.

So it would be interesting to read of work done in LGV/Vicious-walkers and its generalizations that possibly include non-unit step. Of course, once one drops the unit-step requirement, one must also work with a more general definition of "intersection".

I was thinking maybe with the bijection to Young Tableaux, one can obtain a generalization in the Young Tableaux side even though there is no corresponding object at the Vicious walkers side.