One of the most challenging aspects of Lotka-Volterra is in applying it to real-world predator-prey observations. There is always a possibility that an underlying common-mode mechanism is controlling the population instead of non-linear feedback dynamics.

How the mechanism may have been isolated for Lemming/Arctic Fox populations:

https://geoenergymath.com/2020/03/29/lemming-fox-dynamics-not-lotka-volterra/