In the [Lindström–Gessel–Viennot lemma][1] (LGV) the lattice paths are taken to move in unit spatial-steps in unit time.

However, there are [applications][2] ([here][3]) 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][4], one can obtain a generalization in the Young Tableaux side even though there is no corresponding object at the Vicious walkers side.


  [1]: https://en.wikipedia.org/wiki/Lindstr%C3%B6m%E2%80%93Gessel%E2%80%93Viennot_lemma#:~:text=In%20mathematics%2C%20the%20Lindstr%C3%B6m%E2%80%93Gessel,of%20Lindstr%C3%B6m%20published%20in%201973.
  [2]: https://arxiv.org/abs/math-ph/0608056
  [3]: https://arxiv.org/abs/cond-mat/0504417
  [4]: https://www.jstage.jst.go.jp/article/bjsiam/13/4/13_KJ00003574679/_article